(2x-26)(x+4)=180

Solution for (2x-26)(x+4)=180 equation:

(2x-26)(x+4)=180

We move all terms to the left:

(2x-26)(x+4)-(180)=0

We multiply parentheses ..

(+2x^2+8x-26x-104)-180=0

We get rid of parentheses

2x^2+8x-26x-104-180=0

We add all the numbers together, and all the variables

2x^2-18x-284=0

a = 2; b = -18; c = -284;
Δ = b2-4ac
Δ = -182-4·2·(-284)
Δ = 2596
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:

$\sqrt{\Delta}=\sqrt{2596}=\sqrt{4*649}=\sqrt{4}*\sqrt{649}=2\sqrt{649}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{649}}{2*2}=\frac{18-2\sqrt{649}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{649}}{2*2}=\frac{18+2\sqrt{649}}{4}
$