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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 (20+x)/(20+x+18×1.68÷342) = (20-x)/(20-x+18×2.45÷690) .
    Question type: Equation
    Solution:Original question:
     (20 + x ) ÷ (20 + x + 18 ×
42
25
 ÷ 342) = (20 − x ) ÷ (20 − x + 18 ×
49
20
 ÷ 690)
     Multiply both sides of the equation by:(20 + x + 18 ×
42
25
 ÷ 342) ,  (20 − x + 18 ×
49
20
 ÷ 690)
     (20 + x )(20 − x + 18 ×
49
20
 ÷ 690) = (20 − x )(20 + x + 18 ×
42
25
 ÷ 342)
    Remove a bracket on the left of the equation:：
     20(20 − x + 18 ×
49
20
 ÷ 690) + x (20 − x + 18 ×
49
20
 ÷ 690) = (20 − x )(20 + x + 18 ×
42
25
 ÷ 342)
    Remove a bracket on the right of the equation:：
     20(20 − x + 18 ×
49
20
 ÷ 690) + x (20 − x + 18 ×
49
20
 ÷ 690) = 20(20 + x + 18 ×
42
25
 ÷ 342) − x (20 + x + 18 ×
42
25
 ÷ 342)
    Remove a bracket on the left of the equation:
     20 × 20 − 20 x + 20 × 18 ×
49
20
 ÷ 690 + x (20 − x + 18 ×
49
20
 ÷ 690) = 20(20 + x + 18 ×
42
25
 ÷ 342) − x (20 + x + 18 ×
42
25
 ÷ 342)
    Remove a bracket on the right of the equation:：
     20 × 20 − 20 x + 20 × 18 ×
49
20
 ÷ 690 + x (20 − x + 18 ×
49
20
 ÷ 690) = 20 × 20 + 20 x + 20 × 18 ×
42
25
 ÷ 342 − x (20 + x + 18 ×
42
25
 ÷ 342)
    The equation is reduced to :
     400 − 20 x +
147
115
 + x (20 − x + 18 ×
49
20
 ÷ 690) = 400 + 20 x +
168
95
 − x (20 + x + 18 ×
42
25
 ÷ 342)
    The equation is reduced to :
     
46147
115
 − 20 x + x (20 − x + 18 ×
49
20
 ÷ 690) =
38168
95
 + 20 x − x (20 + x + 18 ×
42
25
 ÷ 342)
    Remove a bracket on the left of the equation:
     
46147
115
 − 20 x + x × 20 − x x + x × 18 ×
49
20
 ÷ 690 =
38168
95
 + 20 x − x (20 + x + 18 ×
42
25
 ÷ 342)
    Remove a bracket on the right of the equation:：
     
46147
115
 − 20 x + x × 20 − x x + x × 18 ×
49
20
 ÷ 690 =
38168
95
 + 20 x − x × 20 − x x − x × 18 ×
42
25
 ÷ 342
    The equation is reduced to :
     
46147
115
 − 20 x + x × 20 − x x + x ×
147
2300
 =
38168
95
 + 20 x − x × 20 − x x − x ×
42
475
    The equation is reduced to :
     
46147
115
 +
147
2300
 x − x x =
38168
95
 −
42
475
 x − x x

    After the equation is converted into a general formula, there is a common factor:
    ( 500x - √2588343 )
    From
        500x - √2588343 = 0
    it is concluded that:：
        x1=
√2588343
500

    Solutions that cannot be obtained by factorization:
        x2≈-20.088421 , keep 6 decimal places
        x3≈20.063913 , 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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