18(x-8)(x+2)=180

Solution for 18(x-8)(x+2)=180 equation:

18(x-8)(x+2)=180

We move all terms to the left:

18(x-8)(x+2)-(180)=0

We multiply parentheses ..

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

We multiply parentheses

18x^2+36x-144x-288-180=0

We add all the numbers together, and all the variables

18x^2-108x-468=0

a = 18; b = -108; c = -468;
Δ = b2-4ac
Δ = -1082-4·18·(-468)
Δ = 45360
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:

$\sqrt{\Delta}=\sqrt{45360}=\sqrt{1296*35}=\sqrt{1296}*\sqrt{35}=36\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-36\sqrt{35}}{2*18}=\frac{108-36\sqrt{35}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+36\sqrt{35}}{2*18}=\frac{108+36\sqrt{35}}{36}
$