(x-4)(x+5)=90

Solution for (x-4)(x+5)=90 equation:

(x-4)(x+5)=90

We move all terms to the left:

(x-4)(x+5)-(90)=0

We multiply parentheses ..

(+x^2+5x-4x-20)-90=0

We get rid of parentheses

x^2+5x-4x-20-90=0

We add all the numbers together, and all the variables

x^2+x-110=0

a = 1; b = 1; c = -110;
Δ = b2-4ac
Δ = 12-4·1·(-110)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-21}{2*1}=\frac{-22}{2}
=-11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+21}{2*1}=\frac{20}{2}
=10
$