2x^2-6x-33=0

Solution for 2x^2-6x-33=0 equation:

2x^2-6x-33=0

a = 2; b = -6; c = -33;
Δ = b2-4ac
Δ = -62-4·2·(-33)
Δ = 300
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:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-10\sqrt{3}}{2*2}=\frac{6-10\sqrt{3}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+10\sqrt{3}}{2*2}=\frac{6+10\sqrt{3}}{4}
$