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On line Solution of Monovariate Equation：
    Input any unary equation directly, and then click the "Next" button to obtain the solution of the equation.
    It supports equations that contain mathematical functions.
    Current location：Equations > Monovariate Equation > The history of univariate equation calculation > Answer

    Overview: 1 questions will be solved this time.Among them
           ☆1 equations

[ 1/1 Equation]
    Work: Find the solution of equation 91.20/(1+(x/12*3))+77.52/(1+(x/12*6))+107.92/(1+x) = 246.24 .
    Question type: Equation
    Solution:Original question:
     
456
5
 ÷ (1 + ( x ÷ 12 × 3)) +
1938
25
 ÷ (1 + ( x ÷ 12 × 6)) +
2698
25
 ÷ (1 + x ) =
6156
25
     Multiply both sides of the equation by:(1 + ( x ÷ 12 × 3))
     
456
5
 +
1938
25
 ÷ (1 + ( x ÷ 12 × 6)) × (1 + ( x ÷ 12 × 3)) +
2698
25
 ÷ (1 + x ) × (1 + ( x ÷ 12 × 3)) =
6156
25
(1 + ( x ÷ 12 × 3))
    Remove a bracket on the left of the equation:：
     
456
5
 +
1938
25
 ÷ (1 + ( x ÷ 12 × 6)) × 1 +
1938
25
 ÷ (1 + ( x ÷ 12 × 6)) × ( x ÷ 12 × 3) +
2698
25
 ÷ (1 + x ) × (1 + ( x ÷ 12 × 3)) =
6156
25
(1 + ( x ÷ 12 × 3))
    Remove a bracket on the right of the equation:：
     
456
5
 +
1938
25
 ÷ (1 + ( x ÷ 12 × 6)) × 1 +
1938
25
 ÷ (1 + ( x ÷ 12 × 6)) × ( x ÷ 12 × 3) +
2698
25
 ÷ (1 + x ) × (1 + ( x ÷ 12 × 3)) =
6156
25
 × 1 +
6156
25
( x ÷ 12 × 3)
    The equation is reduced to :
     
456
5
 +
1938
25
 ÷ (1 + ( x ÷ 12 × 6)) +
1938
25
 ÷ (1 + ( x ÷ 12 × 6)) × ( x ÷ 12 × 3) +
2698
25
 ÷ (1 + x ) × (1 + ( x ÷ 12 × 3)) =
6156
25
 +
6156
25
( x ÷ 12 × 3)
     Multiply both sides of the equation by:(1 + ( x ÷ 12 × 6))
     
456
5
(1 + ( x ÷ 12 × 6)) +
1938
25
 +
1938
25
 ÷ (1 + ( x ÷ 12 × 6)) × ( x ÷ 12 × 3)(1 + ( x ÷ 12 × 6)) +
2698
25
 ÷ (1 + x ) × (1 + ( x ÷ 12 × 3))(1 + ( x ÷ 12 × 6)) =
6156
25
(1 + ( x ÷ 12 × 6)) +
6156
25
( x ÷ 12 × 3)(1 + ( x ÷ 12 × 6))
    Remove a bracket on the left of the equation:
     
456
5
 × 1 +
456
5
( x ÷ 12 × 6) +
1938
25
 +
1938
25
 ÷ (1 + ( x ÷ 12 × 6)) × ( x ÷ 12 × 3)(1 + ( x ÷ 12 × 6)) +
2698
25
 ÷ (1 + x ) × (1 + ( x ÷ 12 × 3)) =
6156
25
(1 + ( x ÷ 12 × 6)) +
6156
25
( x ÷ 12 × 3)(1 + ( x ÷ 12 × 6))
    Remove a bracket on the right of the equation:：
     
456
5
 × 1 +
456
5
( x ÷ 12 × 6) +
1938
25
 +
1938
25
 ÷ (1 + ( x ÷ 12 × 6)) × ( x ÷ 12 × 3)(1 + ( x ÷ 12 × 6)) +
2698
25
 ÷ (1 + x ) × (1 + ( x ÷ 12 × 3)) =
6156
25
 × 1 +
6156
25
( x ÷ 12 × 6) +
6156
25
( x ÷ 12 × 3)(1 + ( x ÷ 12 × 6))
    The equation is reduced to :
     
456
5
 +
456
5
( x ÷ 12 × 6) +
1938
25
 +
1938
25
 ÷ (1 + ( x ÷ 12 × 6)) × ( x ÷ 12 × 3)(1 + ( x ÷ 12 × 6)) +
2698
25
 ÷ (1 + x ) × (1 + ( x ÷ 12 × 3))(1 + ( x ÷ 12 × 6)) =
6156
25
 +
6156
25
( x ÷ 12 × 6) +
6156
25
( x ÷ 12 × 3)(1 + ( x ÷ 12 × 6))
    The equation is reduced to :
     
4218
25
 +
456
5
( x ÷ 12 × 6) +
1938
25
 ÷ (1 + ( x ÷ 12 × 6)) × ( x ÷ 12 × 3)(1 + ( x ÷ 12 × 6)) +
2698
25
 ÷ (1 + x ) × (1 + ( x ÷ 12 × 3))(1 + ( x ÷ 12 × 6)) =
6156
25
 +
6156
25
( x ÷ 12 × 6) +
6156
25
( x ÷ 12 × 3)(1 + ( x ÷ 12 × 6))
     Multiply both sides of the equation by:(1 + ( x ÷ 12 × 6))
     
4218
25
(1 + ( x ÷ 12 × 6)) +
456
5
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 6)) +
1938
25
( x ÷ 12 × 3)(1 + ( x ÷ 12 × 6)) +
2698
25
 ÷ (1 + x ) × (1 + ( x ÷ 12 × 3))(1 + ( x ÷ 12 × 6)) =
6156
25
(1 + ( x ÷ 12 × 6)) +
6156
25
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 6)) +
6156
25
( x ÷ 12 × 3)(1 + ( x ÷ 12 × 6))(1 + ( x ÷ 12 × 6))
    Remove a bracket on the left of the equation:
     
4218
25
 × 1 +
4218
25
( x ÷ 12 × 6) +
456
5
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 6)) +
1938
25
( x ÷ 12 × 3)(1 + ( x ÷ 12 × 6)) +
2698
25
 ÷ (1 + x ) =
6156
25
(1 + ( x ÷ 12 × 6)) +
6156
25
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 6)) +
6156
25
( x ÷ 12 × 3)(1 + ( x ÷ 12 × 6))(1 + ( x ÷ 12 × 6))
    Remove a bracket on the right of the equation:：
     
4218
25
 × 1 +
4218
25
( x ÷ 12 × 6) +
456
5
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 6)) +
1938
25
( x ÷ 12 × 3)(1 + ( x ÷ 12 × 6)) +
2698
25
 ÷ (1 + x ) =
6156
25
 × 1 +
6156
25
( x ÷ 12 × 6) +
6156
25
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 6)) +
6156
25
( x ÷ 12 × 3)(1 + ( x ÷ 12 × 6))(1 + ( x ÷ 12 × 6))
    The equation is reduced to :
     
4218
25
 +
4218
25
( x ÷ 12 × 6) +
456
5
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 6)) +
1938
25
( x ÷ 12 × 3)(1 + ( x ÷ 12 × 6)) +
2698
25
 ÷ (1 + x ) × (1 + ( x ÷ 12 × 3)) =
6156
25
 +
6156
25
( x ÷ 12 × 6) +
6156
25
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 6)) +
6156
25
( x ÷ 12 × 3)(1 + ( x ÷ 12 × 6))(1 + ( x ÷ 12 × 6))
     Multiply both sides of the equation by:(1 + x )
     
4218
25
(1 + x ) +
4218
25
( x ÷ 12 × 6)(1 + x ) +
456
5
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 6))(1 + x ) +
1938
25
( x ÷ 12 × 3)(1 + ( x ÷ 12 × 6)) =
6156
25
(1 + x ) +
6156
25
( x ÷ 12 × 6)(1 + x ) +
6156
25
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 6))(1 + x ) +
6156
25
( x ÷ 12 × 3)(1 + ( x ÷ 12 × 6))
    Remove a bracket on the left of the equation:
     
4218
25
 × 1 +
4218
25
 x +
4218
25
( x ÷ 12 × 6)(1 + x ) +
456
5
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 6))(1 + x ) +
1938
25
 =
6156
25
(1 + x ) +
6156
25
( x ÷ 12 × 6)(1 + x ) +
6156
25
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 6))(1 + x ) +
6156
25
( x ÷ 12 × 3)(1 + ( x ÷ 12 × 6))
    Remove a bracket on the right of the equation:：
     
4218
25
 × 1 +
4218
25
 x +
4218
25
( x ÷ 12 × 6)(1 + x ) +
456
5
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 6))(1 + x ) +
1938
25
 =
6156
25
 × 1 +
6156
25
 x +
6156
25
( x ÷ 12 × 6)(1 + x ) +
6156
25
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 6))(1 + x ) +
6156
25
    The equation is reduced to :
     
4218
25
 +
4218
25
 x +
4218
25
( x ÷ 12 × 6)(1 + x ) +
456
5
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 6))(1 + x ) +
1938
25
( x ÷ 12 × 3) =
6156
25
 +
6156
25
 x +
6156
25
( x ÷ 12 × 6)(1 + x ) +
6156
25
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 6))(1 + x ) +
6156
25
( x ÷ 12 × 3)
    Remove a bracket on the left of the equation:
     
4218
25
 +
4218
25
 x +
4218
25
 x ÷ 12 × 6(1 + x ) +
456
5
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 6))(1 + x ) =
6156
25
 +
6156
25
 x +
6156
25
( x ÷ 12 × 6)(1 + x ) +
6156
25
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 6))(1 + x ) +
6156
25
( x ÷ 12 × 3)
    Remove a bracket on the right of the equation:：
     
4218
25
 +
4218
25
 x +
4218
25
 x ÷ 12 × 6(1 + x ) +
456
5
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 6))(1 + x ) =
6156
25
 +
6156
25
 x +
6156
25
 x ÷ 12 × 6(1 + x ) +
6156
25
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 6))(1 + x )
    The equation is reduced to :
     
4218
25
 +
4218
25
 x +
2109
25
 x (1 + x ) +
456
5
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 6))(1 + x ) +
1938
25
( x ÷ 12 × 3) =
6156
25
 +
6156
25
 x +
3078
25
 x (1 + x ) +
6156
25
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 6))(1 + x ) +
6156
25
( x ÷ 12 × 3)
    Remove a bracket on the left of the equation:
     
4218
25
 +
4218
25
 x +
2109
25
 x × 1 +
2109
25
 x x +
456
5
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 6)) =
6156
25
 +
6156
25
 x +
3078
25
 x (1 + x ) +
6156
25
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 6))(1 + x ) +
6156
25
( x ÷ 12 × 3)

    The solution of the equation:
        x1≈-3.153209 , keep 6 decimal places
        x2≈-1.505465 , keep 6 decimal places
        x3≈0.208057 , keep 6 decimal places    
    There are 3 solution(s).

解程的详细方法请参阅：《方程的解法》


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