3y^2-36y-47=0

Solution for 3y^2-36y-47=0 equation:

3y^2-36y-47=0

a = 3; b = -36; c = -47;
Δ = b2-4ac
Δ = -362-4·3·(-47)
Δ = 1860
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:

$\sqrt{\Delta}=\sqrt{1860}=\sqrt{4*465}=\sqrt{4}*\sqrt{465}=2\sqrt{465}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-2\sqrt{465}}{2*3}=\frac{36-2\sqrt{465}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+2\sqrt{465}}{2*3}=\frac{36+2\sqrt{465}}{6}
$