2y(y-12)-33=0

Solution for 2y(y-12)-33=0 equation:

2y(y-12)-33=0

We multiply parentheses

2y^2-24y-33=0

a = 2; b = -24; c = -33;
Δ = b2-4ac
Δ = -242-4·2·(-33)
Δ = 840
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:

$\sqrt{\Delta}=\sqrt{840}=\sqrt{4*210}=\sqrt{4}*\sqrt{210}=2\sqrt{210}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{210}}{2*2}=\frac{24-2\sqrt{210}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{210}}{2*2}=\frac{24+2\sqrt{210}}{4}
$