-2n^2=18n-36

Solution for -2n^2=18n-36 equation:

-2n^2=18n-36

We move all terms to the left:

-2n^2-(18n-36)=0

We get rid of parentheses

-2n^2-18n+36=0

a = -2; b = -18; c = +36;
Δ = b2-4ac
Δ = -182-4·(-2)·36
Δ = 612
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{612}=\sqrt{36*17}=\sqrt{36}*\sqrt{17}=6\sqrt{17}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{17}}{2*-2}=\frac{18-6\sqrt{17}}{-4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{17}}{2*-2}=\frac{18+6\sqrt{17}}{-4}
$