0=-x^2+22x-85

Solution for 0=-x^2+22x-85 equation:

0=-x^2+22x-85

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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