5y(y+3)=3(y+3)

Solution for 5y(y+3)=3(y+3) equation:

5y(y+3)=3(y+3)

We move all terms to the left:

5y(y+3)-(3(y+3))=0

We multiply parentheses

5y^2+15y-(3(y+3))=0


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

3(y+3)

We multiply parentheses

3y+9

Back to the equation:

-(3y+9)


We get rid of parentheses

5y^2+15y-3y-9=0

We add all the numbers together, and all the variables

5y^2+12y-9=0

a = 5; b = 12; c = -9;
Δ = b2-4ac
Δ = 122-4·5·(-9)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-18}{2*5}=\frac{-30}{10}
=-3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+18}{2*5}=\frac{6}{10}
=3/5
$