3x^2-33x+22=0

Solution for 3x^2-33x+22=0 equation:

3x^2-33x+22=0

a = 3; b = -33; c = +22;
Δ = b2-4ac
Δ = -332-4·3·22
Δ = 825
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:

$\sqrt{\Delta}=\sqrt{825}=\sqrt{25*33}=\sqrt{25}*\sqrt{33}=5\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-5\sqrt{33}}{2*3}=\frac{33-5\sqrt{33}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+5\sqrt{33}}{2*3}=\frac{33+5\sqrt{33}}{6}
$