2y^2-8y-33=0

Solution for 2y^2-8y-33=0 equation:

2y^2-8y-33=0

a = 2; b = -8; c = -33;
Δ = b2-4ac
Δ = -82-4·2·(-33)
Δ = 328
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{328}=\sqrt{4*82}=\sqrt{4}*\sqrt{82}=2\sqrt{82}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{82}}{2*2}=\frac{8-2\sqrt{82}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{82}}{2*2}=\frac{8+2\sqrt{82}}{4}
$