x-7=(-2x+20)(-2x+20)

Solution for x-7=(-2x+20)(-2x+20) equation:

x-7=(-2x+20)(-2x+20)

We move all terms to the left:

x-7-((-2x+20)(-2x+20))=0

We multiply parentheses ..

-((+4x^2-40x-40x+400))+x-7=0


We calculate terms in parentheses: -((+4x^2-40x-40x+400)), so:

(+4x^2-40x-40x+400)

We get rid of parentheses

4x^2-40x-40x+400

We add all the numbers together, and all the variables

4x^2-80x+400

Back to the equation:

-(4x^2-80x+400)


We add all the numbers together, and all the variables

x-(4x^2-80x+400)-7=0

We get rid of parentheses

-4x^2+x+80x-400-7=0

We add all the numbers together, and all the variables

-4x^2+81x-407=0

a = -4; b = 81; c = -407;
Δ = b2-4ac
Δ = 812-4·(-4)·(-407)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(81)-7}{2*-4}=\frac{-88}{-8}
=+11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(81)+7}{2*-4}=\frac{-74}{-8}
=9+1/4
$