8x^2-20x-33=0

Solution for 8x^2-20x-33=0 equation:

8x^2-20x-33=0

a = 8; b = -20; c = -33;
Δ = b2-4ac
Δ = -202-4·8·(-33)
Δ = 1456
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:

$\sqrt{\Delta}=\sqrt{1456}=\sqrt{16*91}=\sqrt{16}*\sqrt{91}=4\sqrt{91}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{91}}{2*8}=\frac{20-4\sqrt{91}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{91}}{2*8}=\frac{20+4\sqrt{91}}{16}
$