Y=12+3x-2x^2

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

=12+3Y-2Y^2

We move all terms to the left:

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

We get rid of parentheses

2Y^2-3Y-12=0

a = 2; b = -3; c = -12;
Δ = b2-4ac
Δ = -32-4·2·(-12)
Δ = 105
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{105}}{2*2}=\frac{3-\sqrt{105}}{4}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{105}}{2*2}=\frac{3+\sqrt{105}}{4}
$