(X+4)(x-12)=10

Solution for (X+4)(x-12)=10 equation:

(X+4)(X-12)=10

We move all terms to the left:

(X+4)(X-12)-(10)=0

We multiply parentheses ..

(+X^2-12X+4X-48)-10=0

We get rid of parentheses

X^2-12X+4X-48-10=0

We add all the numbers together, and all the variables

X^2-8X-58=0

a = 1; b = -8; c = -58;
Δ = b2-4ac
Δ = -82-4·1·(-58)
Δ = 296
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:

$\sqrt{\Delta}=\sqrt{296}=\sqrt{4*74}=\sqrt{4}*\sqrt{74}=2\sqrt{74}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{74}}{2*1}=\frac{8-2\sqrt{74}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{74}}{2*1}=\frac{8+2\sqrt{74}}{2}
$