(x+5)(x-12)=18

Solution for (x+5)(x-12)=18 equation:

(x+5)(x-12)=18

We move all terms to the left:

(x+5)(x-12)-(18)=0

We multiply parentheses ..

(+x^2-12x+5x-60)-18=0

We get rid of parentheses

x^2-12x+5x-60-18=0

We add all the numbers together, and all the variables

x^2-7x-78=0

a = 1; b = -7; c = -78;
Δ = b2-4ac
Δ = -72-4·1·(-78)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-19}{2*1}=\frac{-12}{2}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+19}{2*1}=\frac{26}{2}
=13
$