(X+5)(x-3)=-12

Solution for (X+5)(x-3)=-12 equation:

(X+5)(X-3)=-12

We move all terms to the left:

(X+5)(X-3)-(-12)=0

We add all the numbers together, and all the variables

(X+5)(X-3)+12=0

We multiply parentheses ..

(+X^2-3X+5X-15)+12=0

We get rid of parentheses

X^2-3X+5X-15+12=0

We add all the numbers together, and all the variables

X^2+2X-3=0

a = 1; b = 2; c = -3;
Δ = b2-4ac
Δ = 22-4·1·(-3)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-4}{2*1}=\frac{-6}{2}
=-3
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+4}{2*1}=\frac{2}{2}
=1
$