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

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

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

We move all terms to the left:

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

We multiply parentheses

2y^2+18y-(3(y+9))=0


We calculate terms in parentheses: -(3(y+9)), so:

3(y+9)

We multiply parentheses

3y+27

Back to the equation:

-(3y+27)


We get rid of parentheses

2y^2+18y-3y-27=0

We add all the numbers together, and all the variables

2y^2+15y-27=0

a = 2; b = 15; c = -27;
Δ = b2-4ac
Δ = 152-4·2·(-27)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-21}{2*2}=\frac{-36}{4}
=-9
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+21}{2*2}=\frac{6}{4}
=1+1/2
$