6n2-5n=30

Solution for 6n2-5n=30 equation:

6n^2-5n=30

We move all terms to the left:

6n^2-5n-(30)=0

a = 6; b = -5; c = -30;
Δ = b2-4ac
Δ = -52-4·6·(-30)
Δ = 745
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{745}}{2*6}=\frac{5-\sqrt{745}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{745}}{2*6}=\frac{5+\sqrt{745}}{12}
$