(4x-4)(15x-25)=180

Solution for (4x-4)(15x-25)=180 equation:

(4x-4)(15x-25)=180

We move all terms to the left:

(4x-4)(15x-25)-(180)=0

We multiply parentheses ..

(+60x^2-100x-60x+100)-180=0

We get rid of parentheses

60x^2-100x-60x+100-180=0

We add all the numbers together, and all the variables

60x^2-160x-80=0

a = 60; b = -160; c = -80;
Δ = b2-4ac
Δ = -1602-4·60·(-80)
Δ = 44800
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:

$\sqrt{\Delta}=\sqrt{44800}=\sqrt{6400*7}=\sqrt{6400}*\sqrt{7}=80\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-160)-80\sqrt{7}}{2*60}=\frac{160-80\sqrt{7}}{120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-160)+80\sqrt{7}}{2*60}=\frac{160+80\sqrt{7}}{120}
$