2x^2-33x+9=0

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

2x^2-33x+9=0

a = 2; b = -33; c = +9;
Δ = b2-4ac
Δ = -332-4·2·9
Δ = 1017
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:

$\sqrt{\Delta}=\sqrt{1017}=\sqrt{9*113}=\sqrt{9}*\sqrt{113}=3\sqrt{113}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-3\sqrt{113}}{2*2}=\frac{33-3\sqrt{113}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+3\sqrt{113}}{2*2}=\frac{33+3\sqrt{113}}{4}
$