4y^2-9^2=36

Solution for 4y^2-9^2=36 equation:

4y^2-9^2=36

We move all terms to the left:

4y^2-9^2-(36)=0

determiningTheFunctionDomain
4y^2-36-9^2=0

We add all the numbers together, and all the variables

4y^2-117=0

a = 4; b = 0; c = -117;
Δ = b2-4ac
Δ = 02-4·4·(-117)
Δ = 1872
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:

$\sqrt{\Delta}=\sqrt{1872}=\sqrt{144*13}=\sqrt{144}*\sqrt{13}=12\sqrt{13}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{13}}{2*4}=\frac{0-12\sqrt{13}}{8}
=-\frac{12\sqrt{13}}{8}
=-\frac{3\sqrt{13}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{13}}{2*4}=\frac{0+12\sqrt{13}}{8}
=\frac{12\sqrt{13}}{8}
=\frac{3\sqrt{13}}{2}
$