(x+8)(2x-10)=180

Solution for (x+8)(2x-10)=180 equation:

(x+8)(2x-10)=180

We move all terms to the left:

(x+8)(2x-10)-(180)=0

We multiply parentheses ..

(+2x^2-10x+16x-80)-180=0

We get rid of parentheses

2x^2-10x+16x-80-180=0

We add all the numbers together, and all the variables

2x^2+6x-260=0

a = 2; b = 6; c = -260;
Δ = b2-4ac
Δ = 62-4·2·(-260)
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-46}{2*2}=\frac{-52}{4}
=-13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+46}{2*2}=\frac{40}{4}
=10
$