Y-12x+15=3x^2

Solution for Y-12x+15=3x^2 equation:

-12Y+15=3Y^2

We move all terms to the left:

-12Y+15-(3Y^2)=0

determiningTheFunctionDomain
-3Y^2-12Y+15=0

a = -3; b = -12; c = +15;
Δ = b2-4ac
Δ = -122-4·(-3)·15
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-18}{2*-3}=\frac{-6}{-6}
=1
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+18}{2*-3}=\frac{30}{-6}
=-5
$