3y2=36y+81

Solution for 3y2=36y+81 equation:

3y^2=36y+81

We move all terms to the left:

3y^2-(36y+81)=0

We get rid of parentheses

3y^2-36y-81=0

a = 3; b = -36; c = -81;
Δ = b2-4ac
Δ = -362-4·3·(-81)
Δ = 2268
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:

$\sqrt{\Delta}=\sqrt{2268}=\sqrt{324*7}=\sqrt{324}*\sqrt{7}=18\sqrt{7}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-18\sqrt{7}}{2*3}=\frac{36-18\sqrt{7}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+18\sqrt{7}}{2*3}=\frac{36+18\sqrt{7}}{6}
$