3y(y+7)=2(y+9)-y

Solution for 3y(y+7)=2(y+9)-y equation:

3y(y+7)=2(y+9)-y

We move all terms to the left:

3y(y+7)-(2(y+9)-y)=0

We multiply parentheses

3y^2+21y-(2(y+9)-y)=0


We calculate terms in parentheses: -(2(y+9)-y), so:

2(y+9)-y

We add all the numbers together, and all the variables

-1y+2(y+9)

We multiply parentheses

-1y+2y+18

We add all the numbers together, and all the variables

y+18

Back to the equation:

-(y+18)


We get rid of parentheses

3y^2+21y-y-18=0

We add all the numbers together, and all the variables

3y^2+20y-18=0

a = 3; b = 20; c = -18;
Δ = b2-4ac
Δ = 202-4·3·(-18)
Δ = 616
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:

$\sqrt{\Delta}=\sqrt{616}=\sqrt{4*154}=\sqrt{4}*\sqrt{154}=2\sqrt{154}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{154}}{2*3}=\frac{-20-2\sqrt{154}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{154}}{2*3}=\frac{-20+2\sqrt{154}}{6}
$