3y2+2y=4-3y-3y2

Solution for 3y2+2y=4-3y-3y2 equation:

3y^2+2y=4-3y-3y^2

We move all terms to the left:

3y^2+2y-(4-3y-3y^2)=0

We get rid of parentheses

3y^2+3y^2+3y+2y-4=0

We add all the numbers together, and all the variables

6y^2+5y-4=0

a = 6; b = 5; c = -4;
Δ = b2-4ac
Δ = 52-4·6·(-4)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-11}{2*6}=\frac{-16}{12}
=-1+1/3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+11}{2*6}=\frac{6}{12}
=1/2
$