x2+22x+85=0

Solution for x2+22x+85=0 equation:

x2+22x+85=0

We add all the numbers together, and all the variables

x^2+22x+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:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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