67x^2+66x-33=0

Solution for 67x^2+66x-33=0 equation:

67x^2+66x-33=0

a = 67; b = 66; c = -33;
Δ = b2-4ac
Δ = 662-4·67·(-33)
Δ = 13200
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:

$\sqrt{\Delta}=\sqrt{13200}=\sqrt{400*33}=\sqrt{400}*\sqrt{33}=20\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(66)-20\sqrt{33}}{2*67}=\frac{-66-20\sqrt{33}}{134}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(66)+20\sqrt{33}}{2*67}=\frac{-66+20\sqrt{33}}{134}
$