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

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