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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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