33x^2-72x-20=0

Solution for 33x^2-72x-20=0 equation:

33x^2-72x-20=0

a = 33; b = -72; c = -20;
Δ = b2-4ac
Δ = -722-4·33·(-20)
Δ = 7824
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:

$\sqrt{\Delta}=\sqrt{7824}=\sqrt{16*489}=\sqrt{16}*\sqrt{489}=4\sqrt{489}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-4\sqrt{489}}{2*33}=\frac{72-4\sqrt{489}}{66}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+4\sqrt{489}}{2*33}=\frac{72+4\sqrt{489}}{66}
$