3y-2y^2=-6

Solution for 3y-2y^2=-6 equation:

3y-2y^2=-6

We move all terms to the left:

3y-2y^2-(-6)=0

We add all the numbers together, and all the variables

-2y^2+3y+6=0

a = -2; b = 3; c = +6;
Δ = b2-4ac
Δ = 32-4·(-2)·6
Δ = 57
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{57}}{2*-2}=\frac{-3-\sqrt{57}}{-4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{57}}{2*-2}=\frac{-3+\sqrt{57}}{-4}
$