6t^2-30t+33=0

Solution for 6t^2-30t+33=0 equation:

6t^2-30t+33=0

a = 6; b = -30; c = +33;
Δ = b2-4ac
Δ = -302-4·6·33
Δ = 108
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-6\sqrt{3}}{2*6}=\frac{30-6\sqrt{3}}{12}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+6\sqrt{3}}{2*6}=\frac{30+6\sqrt{3}}{12}
$