(4x-6)(8x-6)=180

Solution for (4x-6)(8x-6)=180 equation:

(4x-6)(8x-6)=180

We move all terms to the left:

(4x-6)(8x-6)-(180)=0

We multiply parentheses ..

(+32x^2-24x-48x+36)-180=0

We get rid of parentheses

32x^2-24x-48x+36-180=0

We add all the numbers together, and all the variables

32x^2-72x-144=0

a = 32; b = -72; c = -144;
Δ = b2-4ac
Δ = -722-4·32·(-144)
Δ = 23616
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:

$\sqrt{\Delta}=\sqrt{23616}=\sqrt{576*41}=\sqrt{576}*\sqrt{41}=24\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-24\sqrt{41}}{2*32}=\frac{72-24\sqrt{41}}{64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+24\sqrt{41}}{2*32}=\frac{72+24\sqrt{41}}{64}
$