(X+5)(x-8)=30

Solution for (X+5)(x-8)=30 equation:

(X+5)(X-8)=30

We move all terms to the left:

(X+5)(X-8)-(30)=0

We multiply parentheses ..

(+X^2-8X+5X-40)-30=0

We get rid of parentheses

X^2-8X+5X-40-30=0

We add all the numbers together, and all the variables

X^2-3X-70=0

a = 1; b = -3; c = -70;
Δ = b2-4ac
Δ = -32-4·1·(-70)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-17}{2*1}=\frac{-14}{2}
=-7
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+17}{2*1}=\frac{20}{2}
=10
$