6n^2=-9n+60

Solution for 6n^2=-9n+60 equation:

6n^2=-9n+60

We move all terms to the left:

6n^2-(-9n+60)=0

We get rid of parentheses

6n^2+9n-60=0

a = 6; b = 9; c = -60;
Δ = b2-4ac
Δ = 92-4·6·(-60)
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-39}{2*6}=\frac{-48}{12}
=-4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+39}{2*6}=\frac{30}{12}
=2+1/2
$