(x-5)(x-5)=20x

Solution for (x-5)(x-5)=20x equation:

(x-5)(x-5)=20x

We move all terms to the left:

(x-5)(x-5)-(20x)=0

We add all the numbers together, and all the variables

-20x+(x-5)(x-5)=0

We multiply parentheses ..

(+x^2-5x-5x+25)-20x=0

We get rid of parentheses

x^2-5x-5x-20x+25=0

We add all the numbers together, and all the variables

x^2-30x+25=0

a = 1; b = -30; c = +25;
Δ = b2-4ac
Δ = -302-4·1·25
Δ = 800
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:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-20\sqrt{2}}{2*1}=\frac{30-20\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+20\sqrt{2}}{2*1}=\frac{30+20\sqrt{2}}{2}
$