(4x-4)(x-4)=40

Solution for (4x-4)(x-4)=40 equation:

(4x-4)(x-4)=40

We move all terms to the left:

(4x-4)(x-4)-(40)=0

We multiply parentheses ..

(+4x^2-16x-4x+16)-40=0

We get rid of parentheses

4x^2-16x-4x+16-40=0

We add all the numbers together, and all the variables

4x^2-20x-24=0

a = 4; b = -20; c = -24;
Δ = b2-4ac
Δ = -202-4·4·(-24)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-28}{2*4}=\frac{-8}{8}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+28}{2*4}=\frac{48}{8}
=6
$