X^2=-18x+80

Solution for X^2=-18x+80 equation:

X^2=-18X+80

We move all terms to the left:

X^2-(-18X+80)=0

We get rid of parentheses

X^2+18X-80=0

a = 1; b = 18; c = -80;
Δ = b2-4ac
Δ = 182-4·1·(-80)
Δ = 644
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{644}=\sqrt{4*161}=\sqrt{4}*\sqrt{161}=2\sqrt{161}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{161}}{2*1}=\frac{-18-2\sqrt{161}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{161}}{2*1}=\frac{-18+2\sqrt{161}}{2}
$