4(0)^2-9y^2=144

Solution for 4(0)^2-9y^2=144 equation:

4(0)^2-9y^2=144

We move all terms to the left:

4(0)^2-9y^2-(144)=0

determiningTheFunctionDomain
-9y^2-144+40^2=0

We add all the numbers together, and all the variables

-9y^2+1456=0

a = -9; b = 0; c = +1456;
Δ = b2-4ac
Δ = 02-4·(-9)·1456
Δ = 52416
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:

$\sqrt{\Delta}=\sqrt{52416}=\sqrt{576*91}=\sqrt{576}*\sqrt{91}=24\sqrt{91}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{91}}{2*-9}=\frac{0-24\sqrt{91}}{-18}
=-\frac{24\sqrt{91}}{-18}
=-\frac{4\sqrt{91}}{-3}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{91}}{2*-9}=\frac{0+24\sqrt{91}}{-18}
=\frac{24\sqrt{91}}{-18}
=\frac{4\sqrt{91}}{-3}
$