3n^2+9=12n

Solution for 3n^2+9=12n equation:

3n^2+9=12n

We move all terms to the left:

3n^2+9-(12n)=0

a = 3; b = -12; c = +9;
Δ = b2-4ac
Δ = -122-4·3·9
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6}{2*3}=\frac{6}{6}
=1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6}{2*3}=\frac{18}{6}
=3
$