3y2=15y2-144

Solution for 3y2=15y2-144 equation:

3y^2=15y^2-144

We move all terms to the left:

3y^2-(15y^2-144)=0

We get rid of parentheses

3y^2-15y^2+144=0

We add all the numbers together, and all the variables

-12y^2+144=0

a = -12; b = 0; c = +144;
Δ = b2-4ac
Δ = 02-4·(-12)·144
Δ = 6912
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:

$\sqrt{\Delta}=\sqrt{6912}=\sqrt{2304*3}=\sqrt{2304}*\sqrt{3}=48\sqrt{3}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-48\sqrt{3}}{2*-12}=\frac{0-48\sqrt{3}}{-24}
=-\frac{48\sqrt{3}}{-24}
=-\frac{2\sqrt{3}}{-1}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+48\sqrt{3}}{2*-12}=\frac{0+48\sqrt{3}}{-24}
=\frac{48\sqrt{3}}{-24}
=\frac{2\sqrt{3}}{-1}
$