6n^2-30=11n

Solution for 6n^2-30=11n equation:

6n^2-30=11n

We move all terms to the left:

6n^2-30-(11n)=0

a = 6; b = -11; c = -30;
Δ = b2-4ac
Δ = -112-4·6·(-30)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-29}{2*6}=\frac{-18}{12}
=-1+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+29}{2*6}=\frac{40}{12}
=3+1/3
$