(4x-12)(4x-12)=1600

Solution for (4x-12)(4x-12)=1600 equation:

(4x-12)(4x-12)=1600

We move all terms to the left:

(4x-12)(4x-12)-(1600)=0

We multiply parentheses ..

(+16x^2-48x-48x+144)-1600=0

We get rid of parentheses

16x^2-48x-48x+144-1600=0

We add all the numbers together, and all the variables

16x^2-96x-1456=0

a = 16; b = -96; c = -1456;
Δ = b2-4ac
Δ = -962-4·16·(-1456)
Δ = 102400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{102400}=320$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-320}{2*16}=\frac{-224}{32}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+320}{2*16}=\frac{416}{32}
=13
$