(x-10)(5x-10)=x2-x2

Solution for (x-10)(5x-10)=x2-x2 equation:

(x-10)(5x-10)=x2-x2

We move all terms to the left:

(x-10)(5x-10)-(x2-x2)=0

We add all the numbers together, and all the variables

(x-10)(5x-10)-0=0

We add all the numbers together, and all the variables

(x-10)(5x-10)=0

We multiply parentheses ..

(+5x^2-10x-50x+100)=0

We get rid of parentheses

5x^2-10x-50x+100=0

We add all the numbers together, and all the variables

5x^2-60x+100=0

a = 5; b = -60; c = +100;
Δ = b2-4ac
Δ = -602-4·5·100
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-40}{2*5}=\frac{20}{10}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+40}{2*5}=\frac{100}{10}
=10
$