17=-x^2+18x

Solution for 17=-x^2+18x equation:

17=-x^2+18x

We move all terms to the left:

17-(-x^2+18x)=0

We get rid of parentheses

x^2-18x+17=0

a = 1; b = -18; c = +17;
Δ = b2-4ac
Δ = -182-4·1·17
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-16}{2*1}=\frac{2}{2}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+16}{2*1}=\frac{34}{2}
=17
$