3q^2-12q-20=0

Solution for 3q^2-12q-20=0 equation:

3q^2-12q-20=0

a = 3; b = -12; c = -20;
Δ = b2-4ac
Δ = -122-4·3·(-20)
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-8\sqrt{6}}{2*3}=\frac{12-8\sqrt{6}}{6}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+8\sqrt{6}}{2*3}=\frac{12+8\sqrt{6}}{6}
$