2y^2-68y+264=0

Solution for 2y^2-68y+264=0 equation:

2y^2-68y+264=0

a = 2; b = -68; c = +264;
Δ = b2-4ac
Δ = -682-4·2·264
Δ = 2512
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:

$\sqrt{\Delta}=\sqrt{2512}=\sqrt{16*157}=\sqrt{16}*\sqrt{157}=4\sqrt{157}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-68)-4\sqrt{157}}{2*2}=\frac{68-4\sqrt{157}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-68)+4\sqrt{157}}{2*2}=\frac{68+4\sqrt{157}}{4}
$