(x+2)(x+9)=170

Solution for (x+2)(x+9)=170 equation:

(x+2)(x+9)=170

We move all terms to the left:

(x+2)(x+9)-(170)=0

We multiply parentheses ..

(+x^2+9x+2x+18)-170=0

We get rid of parentheses

x^2+9x+2x+18-170=0

We add all the numbers together, and all the variables

x^2+11x-152=0

a = 1; b = 11; c = -152;
Δ = b2-4ac
Δ = 112-4·1·(-152)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-27}{2*1}=\frac{-38}{2}
=-19
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+27}{2*1}=\frac{16}{2}
=8
$