6n=2n2-9

Solution for 6n=2n2-9 equation:

6n=2n^2-9

We move all terms to the left:

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

We get rid of parentheses

-2n^2+6n+9=0

a = -2; b = 6; c = +9;
Δ = b2-4ac
Δ = 62-4·(-2)·9
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{3}}{2*-2}=\frac{-6-6\sqrt{3}}{-4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{3}}{2*-2}=\frac{-6+6\sqrt{3}}{-4}
$