(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+9x-76=0

a = 1; b = 9; c = -76;
Δ = b2-4ac
Δ = 92-4·1·(-76)
Δ = 385
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{385}}{2*1}=\frac{-9-\sqrt{385}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{385}}{2*1}=\frac{-9+\sqrt{385}}{2}
$