a^2+22a=-85

Solution for a^2+22a=-85 equation:

a^2+22a=-85

We move all terms to the left:

a^2+22a-(-85)=0

We add all the numbers together, and all the variables

a^2+22a+85=0

a = 1; b = 22; c = +85;
Δ = b2-4ac
Δ = 222-4·1·85
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-12}{2*1}=\frac{-34}{2}
=-17
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+12}{2*1}=\frac{-10}{2}
=-5
$