144y^2-7=15

Solution for 144y^2-7=15 equation:

144y^2-7=15

We move all terms to the left:

144y^2-7-(15)=0

We add all the numbers together, and all the variables

144y^2-22=0

a = 144; b = 0; c = -22;
Δ = b2-4ac
Δ = 02-4·144·(-22)
Δ = 12672
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:

$\sqrt{\Delta}=\sqrt{12672}=\sqrt{576*22}=\sqrt{576}*\sqrt{22}=24\sqrt{22}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{22}}{2*144}=\frac{0-24\sqrt{22}}{288}
=-\frac{24\sqrt{22}}{288}
=-\frac{\sqrt{22}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{22}}{2*144}=\frac{0+24\sqrt{22}}{288}
=\frac{24\sqrt{22}}{288}
=\frac{\sqrt{22}}{12}
$