3n^2-17=-11n

Solution for 3n^2-17=-11n equation:

3n^2-17=-11n

We move all terms to the left:

3n^2-17-(-11n)=0

We get rid of parentheses

3n^2+11n-17=0

a = 3; b = 11; c = -17;
Δ = b2-4ac
Δ = 112-4·3·(-17)
Δ = 325
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:

$\sqrt{\Delta}=\sqrt{325}=\sqrt{25*13}=\sqrt{25}*\sqrt{13}=5\sqrt{13}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-5\sqrt{13}}{2*3}=\frac{-11-5\sqrt{13}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+5\sqrt{13}}{2*3}=\frac{-11+5\sqrt{13}}{6}
$