36u^2-27u-14=0

Solution for 36u^2-27u-14=0 equation:

36u^2-27u-14=0

a = 36; b = -27; c = -14;
Δ = b2-4ac
Δ = -272-4·36·(-14)
Δ = 2745
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:

$\sqrt{\Delta}=\sqrt{2745}=\sqrt{9*305}=\sqrt{9}*\sqrt{305}=3\sqrt{305}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-3\sqrt{305}}{2*36}=\frac{27-3\sqrt{305}}{72}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+3\sqrt{305}}{2*36}=\frac{27+3\sqrt{305}}{72}
$