(X+13)(x-5)=-2

Solution for (X+13)(x-5)=-2 equation:

(X+13)(X-5)=-2

We move all terms to the left:

(X+13)(X-5)-(-2)=0

We add all the numbers together, and all the variables

(X+13)(X-5)+2=0

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

X^2+8X-63=0

a = 1; b = 8; c = -63;
Δ = b2-4ac
Δ = 82-4·1·(-63)
Δ = 316
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:

$\sqrt{\Delta}=\sqrt{316}=\sqrt{4*79}=\sqrt{4}*\sqrt{79}=2\sqrt{79}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{79}}{2*1}=\frac{-8-2\sqrt{79}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{79}}{2*1}=\frac{-8+2\sqrt{79}}{2}
$