(x-7)(x+12)=66

Solution for (x-7)(x+12)=66 equation:

(x-7)(x+12)=66

We move all terms to the left:

(x-7)(x+12)-(66)=0

We multiply parentheses ..

(+x^2+12x-7x-84)-66=0

We get rid of parentheses

x^2+12x-7x-84-66=0

We add all the numbers together, and all the variables

x^2+5x-150=0

a = 1; b = 5; c = -150;
Δ = b2-4ac
Δ = 52-4·1·(-150)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-25}{2*1}=\frac{-30}{2}
=-15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+25}{2*1}=\frac{20}{2}
=10
$