(X+5)(x-13)=180

Solution for (X+5)(x-13)=180 equation:

(X+5)(X-13)=180

We move all terms to the left:

(X+5)(X-13)-(180)=0

We multiply parentheses ..

(+X^2-13X+5X-65)-180=0

We get rid of parentheses

X^2-13X+5X-65-180=0

We add all the numbers together, and all the variables

X^2-8X-245=0

a = 1; b = -8; c = -245;
Δ = b2-4ac
Δ = -82-4·1·(-245)
Δ = 1044
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:

$\sqrt{\Delta}=\sqrt{1044}=\sqrt{36*29}=\sqrt{36}*\sqrt{29}=6\sqrt{29}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-6\sqrt{29}}{2*1}=\frac{8-6\sqrt{29}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+6\sqrt{29}}{2*1}=\frac{8+6\sqrt{29}}{2}
$