3y^2+9=81

Solution for 3y^2+9=81 equation:

3y^2+9=81

We move all terms to the left:

3y^2+9-(81)=0

We add all the numbers together, and all the variables

3y^2-72=0

a = 3; b = 0; c = -72;
Δ = b2-4ac
Δ = 02-4·3·(-72)
Δ = 864
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:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{6}}{2*3}=\frac{0-12\sqrt{6}}{6}
=-\frac{12\sqrt{6}}{6}
=-2\sqrt{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{6}}{2*3}=\frac{0+12\sqrt{6}}{6}
=\frac{12\sqrt{6}}{6}
=2\sqrt{6}
$