(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 add all the numbers together, and all the variables

(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-10=0

a = 1; b = -3; c = -10;
Δ = b2-4ac
Δ = -32-4·1·(-10)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-7}{2*1}=\frac{-4}{2}
=-2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+7}{2*1}=\frac{10}{2}
=5
$