(x-3)(x+8)=14

Solution for (x-3)(x+8)=14 equation:

(x-3)(x+8)=14

We move all terms to the left:

(x-3)(x+8)-(14)=0

We multiply parentheses ..

(+x^2+8x-3x-24)-14=0

We get rid of parentheses

x^2+8x-3x-24-14=0

We add all the numbers together, and all the variables

x^2+5x-38=0

a = 1; b = 5; c = -38;
Δ = b2-4ac
Δ = 52-4·1·(-38)
Δ = 177
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{177}}{2*1}=\frac{-5-\sqrt{177}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{177}}{2*1}=\frac{-5+\sqrt{177}}{2}
$