n^2=-12n+9

Solution for n^2=-12n+9 equation:

n^2=-12n+9

We move all terms to the left:

n^2-(-12n+9)=0

We get rid of parentheses

n^2+12n-9=0

a = 1; b = 12; c = -9;
Δ = b2-4ac
Δ = 122-4·1·(-9)
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6\sqrt{5}}{2*1}=\frac{-12-6\sqrt{5}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6\sqrt{5}}{2*1}=\frac{-12+6\sqrt{5}}{2}
$