3y^2+10y+3=2y

Solution for 3y^2+10y+3=2y equation:

3y^2+10y+3=2y

We move all terms to the left:

3y^2+10y+3-(2y)=0

We add all the numbers together, and all the variables

3y^2+8y+3=0

a = 3; b = 8; c = +3;
Δ = b2-4ac
Δ = 82-4·3·3
Δ = 28
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{7}}{2*3}=\frac{-8-2\sqrt{7}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{7}}{2*3}=\frac{-8+2\sqrt{7}}{6}
$