(X+5)(x-3)=180

Solution for (X+5)(x-3)=180 equation:

(X+5)(X-3)=180

We move all terms to the left:

(X+5)(X-3)-(180)=0

We multiply parentheses ..

(+X^2-3X+5X-15)-180=0

We get rid of parentheses

X^2-3X+5X-15-180=0

We add all the numbers together, and all the variables

X^2+2X-195=0

a = 1; b = 2; c = -195;
Δ = b2-4ac
Δ = 22-4·1·(-195)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-28}{2*1}=\frac{-30}{2}
=-15
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+28}{2*1}=\frac{26}{2}
=13
$