(4x-18)(3x-8)=180

Solution for (4x-18)(3x-8)=180 equation:

(4x-18)(3x-8)=180

We move all terms to the left:

(4x-18)(3x-8)-(180)=0

We multiply parentheses ..

(+12x^2-32x-54x+144)-180=0

We get rid of parentheses

12x^2-32x-54x+144-180=0

We add all the numbers together, and all the variables

12x^2-86x-36=0

a = 12; b = -86; c = -36;
Δ = b2-4ac
Δ = -862-4·12·(-36)
Δ = 9124
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:

$\sqrt{\Delta}=\sqrt{9124}=\sqrt{4*2281}=\sqrt{4}*\sqrt{2281}=2\sqrt{2281}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-86)-2\sqrt{2281}}{2*12}=\frac{86-2\sqrt{2281}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-86)+2\sqrt{2281}}{2*12}=\frac{86+2\sqrt{2281}}{24}
$