4x^2+2x-33=0

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

4x^2+2x-33=0

a = 4; b = 2; c = -33;
Δ = b2-4ac
Δ = 22-4·4·(-33)
Δ = 532
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:

$\sqrt{\Delta}=\sqrt{532}=\sqrt{4*133}=\sqrt{4}*\sqrt{133}=2\sqrt{133}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{133}}{2*4}=\frac{-2-2\sqrt{133}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{133}}{2*4}=\frac{-2+2\sqrt{133}}{8}
$