(x-5)(x+8)=14

Solution for (x-5)(x+8)=14 equation:

(x-5)(x+8)=14

We move all terms to the left:

(x-5)(x+8)-(14)=0

We multiply parentheses ..

(+x^2+8x-5x-40)-14=0

We get rid of parentheses

x^2+8x-5x-40-14=0

We add all the numbers together, and all the variables

x^2+3x-54=0

a = 1; b = 3; c = -54;
Δ = b2-4ac
Δ = 32-4·1·(-54)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-15}{2*1}=\frac{-18}{2}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+15}{2*1}=\frac{12}{2}
=6
$