(X-2)(x+7)=90

Solution for (X-2)(x+7)=90 equation:

(X-2)(X+7)=90

We move all terms to the left:

(X-2)(X+7)-(90)=0

We multiply parentheses ..

(+X^2+7X-2X-14)-90=0

We get rid of parentheses

X^2+7X-2X-14-90=0

We add all the numbers together, and all the variables

X^2+5X-104=0

a = 1; b = 5; c = -104;
Δ = b2-4ac
Δ = 52-4·1·(-104)
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{-(5)-21}{2*1}=\frac{-26}{2}
=-13
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+21}{2*1}=\frac{16}{2}
=8
$