n^2=18n-12=0

Solution for n^2=18n-12=0 equation:

n^2=18n-12=0

We move all terms to the left:

n^2-(18n-12)=0

We get rid of parentheses

n^2-18n+12=0

a = 1; b = -18; c = +12;
Δ = b2-4ac
Δ = -182-4·1·12
Δ = 276
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:

$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{69}}{2*1}=\frac{18-2\sqrt{69}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{69}}{2*1}=\frac{18+2\sqrt{69}}{2}
$