6u^2-27u+12=0

Solution for 6u^2-27u+12=0 equation:

6u^2-27u+12=0

a = 6; b = -27; c = +12;
Δ = b2-4ac
Δ = -272-4·6·12
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-21}{2*6}=\frac{6}{12}
=1/2
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+21}{2*6}=\frac{48}{12}
=4
$