3q^2-4q-50=0

Solution for 3q^2-4q-50=0 equation:

3q^2-4q-50=0

a = 3; b = -4; c = -50;
Δ = b2-4ac
Δ = -42-4·3·(-50)
Δ = 616
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:

$\sqrt{\Delta}=\sqrt{616}=\sqrt{4*154}=\sqrt{4}*\sqrt{154}=2\sqrt{154}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{154}}{2*3}=\frac{4-2\sqrt{154}}{6}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{154}}{2*3}=\frac{4+2\sqrt{154}}{6}
$