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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

(x-8)(x+2)-162=0

We multiply parentheses ..

(+x^2+2x-8x-16)-162=0

We get rid of parentheses

x^2+2x-8x-16-162=0

We add all the numbers together, and all the variables

x^2-6x-178=0

a = 1; b = -6; c = -178;
Δ = b2-4ac
Δ = -62-4·1·(-178)
Δ = 748
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:

$\sqrt{\Delta}=\sqrt{748}=\sqrt{4*187}=\sqrt{4}*\sqrt{187}=2\sqrt{187}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{187}}{2*1}=\frac{6-2\sqrt{187}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{187}}{2*1}=\frac{6+2\sqrt{187}}{2}
$