(4x-8)(3x+2)=180

Solution for (4x-8)(3x+2)=180 equation:

(4x-8)(3x+2)=180

We move all terms to the left:

(4x-8)(3x+2)-(180)=0

We multiply parentheses ..

(+12x^2+8x-24x-16)-180=0

We get rid of parentheses

12x^2+8x-24x-16-180=0

We add all the numbers together, and all the variables

12x^2-16x-196=0

a = 12; b = -16; c = -196;
Δ = b2-4ac
Δ = -162-4·12·(-196)
Δ = 9664
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:

$\sqrt{\Delta}=\sqrt{9664}=\sqrt{64*151}=\sqrt{64}*\sqrt{151}=8\sqrt{151}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-8\sqrt{151}}{2*12}=\frac{16-8\sqrt{151}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8\sqrt{151}}{2*12}=\frac{16+8\sqrt{151}}{24}
$