2y^2+10y+6=3y^2+3y+6

Solution for 2y^2+10y+6=3y^2+3y+6 equation:

2y^2+10y+6=3y^2+3y+6

We move all terms to the left:

2y^2+10y+6-(3y^2+3y+6)=0

We get rid of parentheses

2y^2-3y^2+10y-3y-6+6=0

We add all the numbers together, and all the variables

-1y^2+7y=0

a = -1; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-1)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-1}=\frac{-14}{-2}
=+7
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-1}=\frac{0}{-2}
=0
$