(4x-13)(x+8)=180

Solution for (4x-13)(x+8)=180 equation:

(4x-13)(x+8)=180

We move all terms to the left:

(4x-13)(x+8)-(180)=0

We multiply parentheses ..

(+4x^2+32x-13x-104)-180=0

We get rid of parentheses

4x^2+32x-13x-104-180=0

We add all the numbers together, and all the variables

4x^2+19x-284=0

a = 4; b = 19; c = -284;
Δ = b2-4ac
Δ = 192-4·4·(-284)
Δ = 4905
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:

$\sqrt{\Delta}=\sqrt{4905}=\sqrt{9*545}=\sqrt{9}*\sqrt{545}=3\sqrt{545}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-3\sqrt{545}}{2*4}=\frac{-19-3\sqrt{545}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+3\sqrt{545}}{2*4}=\frac{-19+3\sqrt{545}}{8}
$