3n^2-111n=1026

Solution for 3n^2-111n=1026 equation:

3n^2-111n=1026

We move all terms to the left:

3n^2-111n-(1026)=0

a = 3; b = -111; c = -1026;
Δ = b2-4ac
Δ = -1112-4·3·(-1026)
Δ = 24633
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:

$\sqrt{\Delta}=\sqrt{24633}=\sqrt{9*2737}=\sqrt{9}*\sqrt{2737}=3\sqrt{2737}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-111)-3\sqrt{2737}}{2*3}=\frac{111-3\sqrt{2737}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-111)+3\sqrt{2737}}{2*3}=\frac{111+3\sqrt{2737}}{6}
$