(x-5)(x+8)=18

Solution for (x-5)(x+8)=18 equation:

(x-5)(x+8)=18

We move all terms to the left:

(x-5)(x+8)-(18)=0

We multiply parentheses ..

(+x^2+8x-5x-40)-18=0

We get rid of parentheses

x^2+8x-5x-40-18=0

We add all the numbers together, and all the variables

x^2+3x-58=0

a = 1; b = 3; c = -58;
Δ = b2-4ac
Δ = 32-4·1·(-58)
Δ = 241
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{-(3)-\sqrt{241}}{2*1}=\frac{-3-\sqrt{241}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{241}}{2*1}=\frac{-3+\sqrt{241}}{2}
$