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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 (5.67x+100+5.67)*(1.5x+100)/(5.67x+100)/(1.5x+100+1.5) = (20000/49+(x+1)*x)/(20000/49+x*x) .
    Question type: Equation
    Solution:Original question:
     (
567
100
 x + 100 +
567
100
)(
3
2
 x + 100) ÷ (
567
100
 x + 100) ÷ (
3
2
 x + 100 +
3
2
) = (20000 ÷ 49 + ( x + 1) x ) ÷ (20000 ÷ 49 + x x )
     Multiply both sides of the equation by:(
567
100
 x + 100) ,  (20000 ÷ 49 + x x )
     (
567
100
 x + 100 +
567
100
)(
3
2
 x + 100) ÷ (
3
2
 x + 100 +
3
2
) × (20000 ÷ 49 + x x ) = (20000 ÷ 49 + ( x + 1) x )(
567
100
 x + 100)
    Remove a bracket on the left of the equation:：
     
567
100
 x (
3
2
 x + 100) ÷ (
3
2
 x + 100 +
3
2
) × (20000 ÷ 49 + x x ) + 100(
3
2
 x + 100) ÷ (
3
2
 x + 100 +
3
2
) × (20000 ÷ 49 + x x ) +
567
100
(
3
2
 x + 100) ÷ (
3
2
 x + 100 +
3
2
) = (20000 ÷ 49 + ( x + 1) x )(
567
100
 x + 100)
    Remove a bracket on the right of the equation:：
     
567
100
 x (
3
2
 x + 100) ÷ (
3
2
 x + 100 +
3
2
) × (20000 ÷ 49 + x x ) + 100(
3
2
 x + 100) ÷ (
3
2
 x + 100 +
3
2
) × (20000 ÷ 49 + x x ) +
567
100
(
3
2
 x + 100) ÷ (
3
2
 x + 100 +
3
2
) = 20000 ÷ 49 × (
567
100
 x + 100) + ( x + 1) x (
567
100
 x + 100)
    The equation is reduced to :
     
567
100
 x (
3
2
 x + 100) ÷ (
3
2
 x + 100 +
3
2
) × (20000 ÷ 49 + x x ) + 100(
3
2
 x + 100) ÷ (
3
2
 x + 100 +
3
2
) × (20000 ÷ 49 + x x ) +
567
100
(
3
2
 x + 100) ÷ (
3
2
 x + 100 +
3
2
) =
20000
49
(
567
100
 x + 100) + ( x + 1) x (
567
100
 x + 100)
     Multiply both sides of the equation by:(
3
2
 x + 100 +
3
2
)
     
567
100
 x (
3
2
 x + 100)(20000 ÷ 49 + x x ) + 100(
3
2
 x + 100)(20000 ÷ 49 + x x ) +
567
100
(
3
2
 x + 100)(20000 ÷ 49 + x x ) =
20000
49
(
567
100
 x + 100)(
3
2
 x + 100 +
3
2
) + ( x + 1) x (
567
100
 x + 100)(
3
2
 x + 100 +
3
2
)
    Remove a bracket on the left of the equation:
     
567
100
 x ×
3
2
 x (20000 ÷ 49 + x x ) +
567
100
 x × 100(20000 ÷ 49 + x x ) + 100(
3
2
 x + 100)(20000 ÷ 49 + x x ) =
20000
49
(
567
100
 x + 100)(
3
2
 x + 100 +
3
2
) + ( x + 1) x (
567
100
 x + 100)(
3
2
 x + 100 +
3
2
)
    Remove a bracket on the right of the equation:：
     
567
100
 x ×
3
2
 x (20000 ÷ 49 + x x ) +
567
100
 x × 100(20000 ÷ 49 + x x ) + 100(
3
2
 x + 100)(20000 ÷ 49 + x x ) =
20000
49
 ×
567
100
 x (
3
2
 x + 100 +
3
2
) +
20000
49
 × 100(
3
2
 x + 100 +
3
2
) + ( x + 1) x (
567
100
 x + 100)(
3
2
 x + 100 +
3
2
)
    The equation is reduced to :
     
1701
200
 x x (20000 ÷ 49 + x x ) + 567 x (20000 ÷ 49 + x x ) + 100(
3
2
 x + 100)(20000 ÷ 49 + x x ) +
567
100
(
3
2
 x + 100) =
16200
7
 x (
3
2
 x + 100 +
3
2
) +
2000000
49
(
3
2
 x + 100 +
3
2
) + ( x + 1) x (
567
100
 x + 100)(
3
2
 x + 100 +
3
2
)
    Remove a bracket on the left of the equation:
     
1701
200
 x x × 20000 ÷ 49 +
1701
200
 x x x x + 567 x =
16200
7
 x (
3
2
 x + 100 +
3
2
) +
2000000
49
(
3
2
 x + 100 +
3
2
) + ( x + 1) x (
567
100
 x + 100)(
3
2
 x + 100 +
3
2
)
    Remove a bracket on the right of the equation:：
     
1701
200
 x x × 20000 ÷ 49 +
1701
200
 x x x x + 567 x =
16200
7
 x ×
3
2
 x +
16200
7
 x × 100 +
16200
7
 x ×
3
2
 +
2000000
49
(
3
2
 x + 100 +
3
2
)
    The equation is reduced to :
     
24300
7
 x x +
1701
200
 x x x x + 567 x (20000 ÷ 49 + x x ) + 100 =
24300
7
 x x +
1620000
7
 x +
24300
7
 x +
2000000
49
(
3
2
 x + 100 +
3
2
) + ( x + 1) x (
567
100
 x + 100)
    The equation is reduced to :
     
24300
7
 x x +
1701
200
 x x x x + 567 x (20000 ÷ 49 + x x ) + 100 =
24300
7
 x x + 234900 x +
2000000
49
(
3
2
 x + 100 +
3
2
) + ( x + 1) x (
567
100
 x + 100)(
3
2
 x + 100 +
3
2
)
    Remove a bracket on the left of the equation:
     
24300
7
 x x +
1701
200
 x x x x + 567 x × 20000 ÷ 49 =
24300
7
 x x + 234900 x +
2000000
49
(
3
2
 x + 100 +
3
2
) + ( x + 1) x (
567
100
 x + 100)(
3
2
 x + 100 +
3
2
)
    Remove a bracket on the right of the equation:：
     
24300
7
 x x +
1701
200
 x x x x + 567 x × 20000 ÷ 49 =
24300
7
 x x + 234900 x +
2000000
49
 ×
3
2
 x +
2000000
49
 × 100 +
2000000
49
 ×
3
2
    The equation is reduced to :
     
24300
7
 x x +
1701
200
 x x x x +
1620000
7
 x + 567 x =
24300
7
 x x + 234900 x +
3000000
49
 x +
200000000
49
 +
3000000
49
 + ( x + 1) x (
567
100
 x + 100)
    The equation is reduced to :
     
24300
7
 x x +
1701
200
 x x x x +
1620000
7
 x + 567 x =
24300
7
 x x +
14510100
49
 x +
29000000
7
 + ( x + 1) x (
567
100
 x + 100)(
3
2
 x + 100 +
3
2
)
    Remove a bracket on the left of the equation:
     
24300
7
 x x +
1701
200
 x x x x +
1620000
7
 x + 567 x =
24300
7
 x x +
14510100
49
 x +
29000000
7
 + ( x + 1) x (
567
100
 x + 100)(
3
2
 x + 100 +
3
2
)
    Remove a bracket on the right of the equation:：
     
24300
7
 x x +
1701
200
 x x x x +
1620000
7
 x + 567 x =
24300
7
 x x +
14510100
49
 x +
29000000
7
 + x x (
567
100
 x + 100)(
3
2
 x + 100 +
3
2
) + 1 x
    The equation is reduced to :
     
24300
7
 x x +
1701
200
 x x x x +
1620000
7
 x + 567 x =
24300
7
 x x +
14510100
49
 x +
29000000
7
 + x x (
567
100
 x + 100)(
3
2
 x + 100 +
3
2
) + 1 x
    Remove a bracket on the left of the equation:
     
24300
7
 x x +
1701
200
 x x x x +
1620000
7
 x + 567 x =
24300
7
 x x +
14510100
49
 x +
29000000
7
 + x x (
567
100
 x + 100)(
3
2
 x + 100 +
3
2
) + 1 x
    Remove a bracket on the right of the equation:：
     
24300
7
 x x +
1701
200
 x x x x +
1620000
7
 x + 567 x =
24300
7
 x x +
14510100
49
 x +
29000000
7
 + x x ×
567
100
 x (
3
2
 x + 100 +
3
2
) + x
    The equation is reduced to :
     
24300
7
 x x +
1701
200
 x x x x +
1620000
7
 x + 567 x =
24300
7
 x x +
14510100
49
 x +
29000000
7
 + x x ×
567
100
 x (
3
2
 x + 100 +
3
2
) + x

    After the equation is converted into a general formula, there is a common factor:
    ( √200000x - √26392957 )
    From
        √200000x - √26392957 = 0
    it is concluded that:：
        x1=
√26392957
√200000

    Solutions that cannot be obtained by factorization:
        x2≈-17.636684 , keep 6 decimal places    
    There are 2 solution(s).

解程的详细方法请参阅：《方程的解法》


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