30u^2+21u-6=0

Solution for 30u^2+21u-6=0 equation:

30u^2+21u-6=0

a = 30; b = 21; c = -6;
Δ = b2-4ac
Δ = 212-4·30·(-6)
Δ = 1161
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1161}=\sqrt{9*129}=\sqrt{9}*\sqrt{129}=3\sqrt{129}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-3\sqrt{129}}{2*30}=\frac{-21-3\sqrt{129}}{60}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+3\sqrt{129}}{2*30}=\frac{-21+3\sqrt{129}}{60}
$