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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 84.5/(1+(x/12*6))+0.325/(1+(x/12*13)) = 78.325 .
    Question type: Equation
    Solution:Original question:
     
169
2
 ÷ (1 + ( x ÷ 12 × 6)) +
13
40
 ÷ (1 + ( x ÷ 12 × 13)) =
3133
40
     Multiply both sides of the equation by:(1 + ( x ÷ 12 × 6))
     
169
2
 +
13
40
 ÷ (1 + ( x ÷ 12 × 13)) × (1 + ( x ÷ 12 × 6)) =
3133
40
(1 + ( x ÷ 12 × 6))
    Remove a bracket on the left of the equation:：
     
169
2
 +
13
40
 ÷ (1 + ( x ÷ 12 × 13)) × 1 +
13
40
 ÷ (1 + ( x ÷ 12 × 13)) × ( x ÷ 12 × 6) =
3133
40
(1 + ( x ÷ 12 × 6))
    Remove a bracket on the right of the equation:：
     
169
2
 +
13
40
 ÷ (1 + ( x ÷ 12 × 13)) × 1 +
13
40
 ÷ (1 + ( x ÷ 12 × 13)) × ( x ÷ 12 × 6) =
3133
40
 × 1 +
3133
40
( x ÷ 12 × 6)
    The equation is reduced to :
     
169
2
 +
13
40
 ÷ (1 + ( x ÷ 12 × 13)) +
13
40
 ÷ (1 + ( x ÷ 12 × 13)) × ( x ÷ 12 × 6) =
3133
40
 +
3133
40
( x ÷ 12 × 6)
     Multiply both sides of the equation by:(1 + ( x ÷ 12 × 13))
     
169
2
(1 + ( x ÷ 12 × 13)) +
13
40
 +
13
40
 ÷ (1 + ( x ÷ 12 × 13)) × ( x ÷ 12 × 6)(1 + ( x ÷ 12 × 13)) =
3133
40
(1 + ( x ÷ 12 × 13)) +
3133
40
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 13))
    Remove a bracket on the left of the equation:
     
169
2
 × 1 +
169
2
( x ÷ 12 × 13) +
13
40
 +
13
40
 ÷ (1 + ( x ÷ 12 × 13)) × ( x ÷ 12 × 6)(1 + ( x ÷ 12 × 13)) =
3133
40
(1 + ( x ÷ 12 × 13)) +
3133
40
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 13))
    Remove a bracket on the right of the equation:：
     
169
2
 × 1 +
169
2
( x ÷ 12 × 13) +
13
40
 +
13
40
 ÷ (1 + ( x ÷ 12 × 13)) × ( x ÷ 12 × 6)(1 + ( x ÷ 12 × 13)) =
3133
40
 × 1 +
3133
40
( x ÷ 12 × 13) +
3133
40
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 13))
    The equation is reduced to :
     
169
2
 +
169
2
( x ÷ 12 × 13) +
13
40
 +
13
40
 ÷ (1 + ( x ÷ 12 × 13)) × ( x ÷ 12 × 6)(1 + ( x ÷ 12 × 13)) =
3133
40
 +
3133
40
( x ÷ 12 × 13) +
3133
40
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 13))
    The equation is reduced to :
     
3393
40
 +
169
2
( x ÷ 12 × 13) +
13
40
 ÷ (1 + ( x ÷ 12 × 13)) × ( x ÷ 12 × 6)(1 + ( x ÷ 12 × 13)) =
3133
40
 +
3133
40
( x ÷ 12 × 13) +
3133
40
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 13))
     Multiply both sides of the equation by:(1 + ( x ÷ 12 × 13))
     
3393
40
(1 + ( x ÷ 12 × 13)) +
169
2
( x ÷ 12 × 13)(1 + ( x ÷ 12 × 13)) +
13
40
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 13)) =
3133
40
(1 + ( x ÷ 12 × 13)) +
3133
40
( x ÷ 12 × 13)(1 + ( x ÷ 12 × 13)) +
3133
40
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 13))(1 + ( x ÷ 12 × 13))
    Remove a bracket on the left of the equation:
     
3393
40
 × 1 +
3393
40
( x ÷ 12 × 13) +
169
2
( x ÷ 12 × 13)(1 + ( x ÷ 12 × 13)) +
13
40
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 13)) =
3133
40
(1 + ( x ÷ 12 × 13)) +
3133
40
( x ÷ 12 × 13)(1 + ( x ÷ 12 × 13)) +
3133
40
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 13))(1 + ( x ÷ 12 × 13))
    Remove a bracket on the right of the equation:：
     
3393
40
 × 1 +
3393
40
( x ÷ 12 × 13) +
169
2
( x ÷ 12 × 13)(1 + ( x ÷ 12 × 13)) +
13
40
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 13)) =
3133
40
 × 1 +
3133
40
( x ÷ 12 × 13) +
3133
40
( x ÷ 12 × 13)(1 + ( x ÷ 12 × 13)) +
3133
40
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 13))(1 + ( x ÷ 12 × 13))
    The equation is reduced to :
     
3393
40
 +
3393
40
( x ÷ 12 × 13) +
169
2
( x ÷ 12 × 13)(1 + ( x ÷ 12 × 13)) +
13
40
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 13)) =
3133
40
 +
3133
40
( x ÷ 12 × 13) +
3133
40
( x ÷ 12 × 13)(1 + ( x ÷ 12 × 13)) +
3133
40
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 13))(1 + ( x ÷ 12 × 13))
    Remove a bracket on the left of the equation:
     
3393
40
 +
3393
40
 x ÷ 12 × 13 +
169
2
( x ÷ 12 × 13)(1 + ( x ÷ 12 × 13)) +
13
40
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 13)) =
3133
40
 +
3133
40
( x ÷ 12 × 13) +
3133
40
( x ÷ 12 × 13)(1 + ( x ÷ 12 × 13)) +
3133
40
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 13))(1 + ( x ÷ 12 × 13))
    Remove a bracket on the right of the equation:：
     
3393
40
 +
3393
40
 x ÷ 12 × 13 +
169
2
( x ÷ 12 × 13)(1 + ( x ÷ 12 × 13)) +
13
40
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 13)) =
3133
40
 +
3133
40
 x ÷ 12 × 13 +
3133
40
( x ÷ 12 × 13)(1 + ( x ÷ 12 × 13)) +
3133
40
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 13))(1 + ( x ÷ 12 × 13))
    The equation is reduced to :
     
3393
40
 +
14703
160
 x +
169
2
( x ÷ 12 × 13)(1 + ( x ÷ 12 × 13)) +
13
40
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 13)) =
3133
40
 +
40729
480
 x +
3133
40
( x ÷ 12 × 13)(1 + ( x ÷ 12 × 13)) +
3133
40
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 13))(1 + ( x ÷ 12 × 13))
    Remove a bracket on the left of the equation:
     
3393
40
 +
14703
160
 x +
169
2
 x ÷ 12 × 13(1 + ( x ÷ 12 × 13)) +
13
40
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 13)) =
3133
40
 +
40729
480
 x +
3133
40
( x ÷ 12 × 13)(1 + ( x ÷ 12 × 13)) +
3133
40
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 13))(1 + ( x ÷ 12 × 13))
    Remove a bracket on the right of the equation:：
     
3393
40
 +
14703
160
 x +
169
2
 x ÷ 12 × 13(1 + ( x ÷ 12 × 13)) +
13
40
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 13)) =
3133
40
 +
40729
480
 x +
3133
40
 x ÷ 12 × 13(1 + ( x ÷ 12 × 13)) +
3133
40
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 13))(1 + ( x ÷ 12 × 13))
    The equation is reduced to :
     
3393
40
 +
14703
160
 x +
2197
24
 x (1 + ( x ÷ 12 × 13)) +
13
40
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 13)) =
3133
40
 +
40729
480
 x +
40729
480
 x (1 + ( x ÷ 12 × 13)) +
3133
40
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 13))(1 + ( x ÷ 12 × 13))
    Remove a bracket on the left of the equation:
     
3393
40
 +
14703
160
 x +
2197
24
 x × 1 +
2197
24
 x ( x ÷ 12 × 13) +
13
40
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 13)) =
3133
40
 +
40729
480
 x +
40729
480
 x (1 + ( x ÷ 12 × 13)) +
3133
40
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 13))(1 + ( x ÷ 12 × 13))
    Remove a bracket on the right of the equation:：
     
3393
40
 +
14703
160
 x +
2197
24
 x × 1 +
2197
24
 x ( x ÷ 12 × 13) +
13
40
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 13)) =
3133
40
 +
40729
480
 x +
40729
480
 x × 1 +
40729
480
 x ( x ÷ 12 × 13) +
3133
40
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 13))
    The equation is reduced to :
     
3393
40
 +
14703
160
 x +
2197
24
 x +
2197
24
 x ( x ÷ 12 × 13) +
13
40
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 13)) =
3133
40
 +
40729
480
 x +
40729
480
 x +
40729
480
 x ( x ÷ 12 × 13) +
3133
40
( x ÷ 12 × 6)(1 + ( x ÷ 12 × 13))(1 + ( x ÷ 12 × 13))

    
        x≈0.165296 , keep 6 decimal places    
    There are 1 solution(s).

解一元一次方程的详细方法请参阅：《一元一次方程的解法》


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