4y^2+36y=81

Solution for 4y^2+36y=81 equation:

4y^2+36y=81

We move all terms to the left:

4y^2+36y-(81)=0

a = 4; b = 36; c = -81;
Δ = b2-4ac
Δ = 362-4·4·(-81)
Δ = 2592
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:

$\sqrt{\Delta}=\sqrt{2592}=\sqrt{1296*2}=\sqrt{1296}*\sqrt{2}=36\sqrt{2}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36\sqrt{2}}{2*4}=\frac{-36-36\sqrt{2}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36\sqrt{2}}{2*4}=\frac{-36+36\sqrt{2}}{8}
$