n^2-18n=-11

Solution for n^2-18n=-11 equation:

n^2-18n=-11

We move all terms to the left:

n^2-18n-(-11)=0

We add all the numbers together, and all the variables

n^2-18n+11=0

a = 1; b = -18; c = +11;
Δ = b2-4ac
Δ = -182-4·1·11
Δ = 280
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:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{70}}{2*1}=\frac{18-2\sqrt{70}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{70}}{2*1}=\frac{18+2\sqrt{70}}{2}
$