4y2+12y+9=X^2

Solution for 4y2+12y+9=X^2 equation:

4y^2+12y+9=y^2

We move all terms to the left:

4y^2+12y+9-(y^2)=0

determiningTheFunctionDomain
4y^2-y^2+12y+9=0

We add all the numbers together, and all the variables

3y^2+12y+9=0

a = 3; b = 12; c = +9;
Δ = b2-4ac
Δ = 122-4·3·9
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6}{2*3}=\frac{-18}{6}
=-3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6}{2*3}=\frac{-6}{6}
=-1
$