3u^2+27u-45=0

Solution for 3u^2+27u-45=0 equation:

3u^2+27u-45=0

a = 3; b = 27; c = -45;
Δ = b2-4ac
Δ = 272-4·3·(-45)
Δ = 1269
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:

$\sqrt{\Delta}=\sqrt{1269}=\sqrt{9*141}=\sqrt{9}*\sqrt{141}=3\sqrt{141}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-3\sqrt{141}}{2*3}=\frac{-27-3\sqrt{141}}{6}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+3\sqrt{141}}{2*3}=\frac{-27+3\sqrt{141}}{6}
$