x=102x-20/x-10

Solution for x=102x-20/x-10 equation:

x=102x-20/x-10

We move all terms to the left:

x-(102x-20/x-10)=0


Domain of the equation: x-10)!=0

x∈R


We get rid of parentheses

x-102x+20/x+10=0

We multiply all the terms by the denominator


x*x-102x*x+10*x+20=0

We add all the numbers together, and all the variables

10x+x*x-102x*x+20=0

Wy multiply elements

x^2-102x^2+10x+20=0

We add all the numbers together, and all the variables

-101x^2+10x+20=0

a = -101; b = 10; c = +20;
Δ = b2-4ac
Δ = 102-4·(-101)·20
Δ = 8180
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8180}=\sqrt{4*2045}=\sqrt{4}*\sqrt{2045}=2\sqrt{2045}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{2045}}{2*-101}=\frac{-10-2\sqrt{2045}}{-202}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{2045}}{2*-101}=\frac{-10+2\sqrt{2045}}{-202}
$