6u^2-3u-15=0

Solution for 6u^2-3u-15=0 equation:

6u^2-3u-15=0

a = 6; b = -3; c = -15;
Δ = b2-4ac
Δ = -32-4·6·(-15)
Δ = 369
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:

$\sqrt{\Delta}=\sqrt{369}=\sqrt{9*41}=\sqrt{9}*\sqrt{41}=3\sqrt{41}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{41}}{2*6}=\frac{3-3\sqrt{41}}{12}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{41}}{2*6}=\frac{3+3\sqrt{41}}{12}
$