33x^2-33x-9=0

Solution for 33x^2-33x-9=0 equation:

33x^2-33x-9=0

a = 33; b = -33; c = -9;
Δ = b2-4ac
Δ = -332-4·33·(-9)
Δ = 2277
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2277}=\sqrt{9*253}=\sqrt{9}*\sqrt{253}=3\sqrt{253}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-3\sqrt{253}}{2*33}=\frac{33-3\sqrt{253}}{66}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+3\sqrt{253}}{2*33}=\frac{33+3\sqrt{253}}{66}
$