-12q^2+60q-2=0

Solution for -12q^2+60q-2=0 equation:

-12q^2+60q-2=0

a = -12; b = 60; c = -2;
Δ = b2-4ac
Δ = 602-4·(-12)·(-2)
Δ = 3504
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3504}=\sqrt{16*219}=\sqrt{16}*\sqrt{219}=4\sqrt{219}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-4\sqrt{219}}{2*-12}=\frac{-60-4\sqrt{219}}{-24}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+4\sqrt{219}}{2*-12}=\frac{-60+4\sqrt{219}}{-24}
$