12n^2-60n-45=0

Solution for 12n^2-60n-45=0 equation:

12n^2-60n-45=0

a = 12; b = -60; c = -45;
Δ = b2-4ac
Δ = -602-4·12·(-45)
Δ = 5760
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:

$\sqrt{\Delta}=\sqrt{5760}=\sqrt{576*10}=\sqrt{576}*\sqrt{10}=24\sqrt{10}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-24\sqrt{10}}{2*12}=\frac{60-24\sqrt{10}}{24}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+24\sqrt{10}}{2*12}=\frac{60+24\sqrt{10}}{24}
$