3n^2=6n+9=0

Solution for 3n^2=6n+9=0 equation:

3n^2=6n+9=0

We move all terms to the left:

3n^2-(6n+9)=0

We get rid of parentheses

3n^2-6n-9=0

a = 3; b = -6; c = -9;
Δ = b2-4ac
Δ = -62-4·3·(-9)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-12}{2*3}=\frac{-6}{6}
=-1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+12}{2*3}=\frac{18}{6}
=3
$