4y2-147=y2

Solution for 4y2-147=y2 equation:

4y^2-147=y2

We move all terms to the left:

4y^2-147-(y2)=0

We add all the numbers together, and all the variables

3y^2-147=0

a = 3; b = 0; c = -147;
Δ = b2-4ac
Δ = 02-4·3·(-147)
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-42}{2*3}=\frac{-42}{6}
=-7
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+42}{2*3}=\frac{42}{6}
=7
$