3q^2-30q+10=0

Solution for 3q^2-30q+10=0 equation:

3q^2-30q+10=0

a = 3; b = -30; c = +10;
Δ = b2-4ac
Δ = -302-4·3·10
Δ = 780
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:

$\sqrt{\Delta}=\sqrt{780}=\sqrt{4*195}=\sqrt{4}*\sqrt{195}=2\sqrt{195}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{195}}{2*3}=\frac{30-2\sqrt{195}}{6}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{195}}{2*3}=\frac{30+2\sqrt{195}}{6}
$