(4x-1)(3x-8)=180

Solution for (4x-1)(3x-8)=180 equation:

(4x-1)(3x-8)=180

We move all terms to the left:

(4x-1)(3x-8)-(180)=0

We multiply parentheses ..

(+12x^2-32x-3x+8)-180=0

We get rid of parentheses

12x^2-32x-3x+8-180=0

We add all the numbers together, and all the variables

12x^2-35x-172=0

a = 12; b = -35; c = -172;
Δ = b2-4ac
Δ = -352-4·12·(-172)
Δ = 9481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-\sqrt{9481}}{2*12}=\frac{35-\sqrt{9481}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+\sqrt{9481}}{2*12}=\frac{35+\sqrt{9481}}{24}
$