3y^2-36y+44=0

Solution for 3y^2-36y+44=0 equation:

3y^2-36y+44=0

a = 3; b = -36; c = +44;
Δ = b2-4ac
Δ = -362-4·3·44
Δ = 768
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:

$\sqrt{\Delta}=\sqrt{768}=\sqrt{256*3}=\sqrt{256}*\sqrt{3}=16\sqrt{3}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-16\sqrt{3}}{2*3}=\frac{36-16\sqrt{3}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+16\sqrt{3}}{2*3}=\frac{36+16\sqrt{3}}{6}
$