3a2-6a-33=0

Solution for 3a2-6a-33=0 equation:

3a^2-6a-33=0

a = 3; b = -6; c = -33;
Δ = b2-4ac
Δ = -62-4·3·(-33)
Δ = 432
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-12\sqrt{3}}{2*3}=\frac{6-12\sqrt{3}}{6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+12\sqrt{3}}{2*3}=\frac{6+12\sqrt{3}}{6}
$