(X+4)(x-12)=5

Solution for (X+4)(x-12)=5 equation:

(X+4)(X-12)=5

We move all terms to the left:

(X+4)(X-12)-(5)=0

We multiply parentheses ..

(+X^2-12X+4X-48)-5=0

We get rid of parentheses

X^2-12X+4X-48-5=0

We add all the numbers together, and all the variables

X^2-8X-53=0

a = 1; b = -8; c = -53;
Δ = b2-4ac
Δ = -82-4·1·(-53)
Δ = 276
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:

$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{69}}{2*1}=\frac{8-2\sqrt{69}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{69}}{2*1}=\frac{8+2\sqrt{69}}{2}
$