12y^-2+3y^2-15=0

Solution for 12y^-2+3y^2-15=0 equation:

12y^-2+3y^2-15=0

We add all the numbers together, and all the variables

3y^2+12y-17=0

a = 3; b = 12; c = -17;
Δ = b2-4ac
Δ = 122-4·3·(-17)
Δ = 348
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:

$\sqrt{\Delta}=\sqrt{348}=\sqrt{4*87}=\sqrt{4}*\sqrt{87}=2\sqrt{87}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{87}}{2*3}=\frac{-12-2\sqrt{87}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{87}}{2*3}=\frac{-12+2\sqrt{87}}{6}
$