6x^2+4x-33=0

Solution for 6x^2+4x-33=0 equation:

6x^2+4x-33=0

a = 6; b = 4; c = -33;
Δ = b2-4ac
Δ = 42-4·6·(-33)
Δ = 808
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:

$\sqrt{\Delta}=\sqrt{808}=\sqrt{4*202}=\sqrt{4}*\sqrt{202}=2\sqrt{202}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{202}}{2*6}=\frac{-4-2\sqrt{202}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{202}}{2*6}=\frac{-4+2\sqrt{202}}{12}
$