y+3=2y2

Solution for y+3=2y2 equation:

y+3=2y^2

We move all terms to the left:

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

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

a = -2; b = 1; c = +3;
Δ = b2-4ac
Δ = 12-4·(-2)·3
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-5}{2*-2}=\frac{-6}{-4}
=1+1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+5}{2*-2}=\frac{4}{-4}
=-1
$