5y(y+9)=3(y+9)

Solution for 5y(y+9)=3(y+9) equation:

5y(y+9)=3(y+9)

We move all terms to the left:

5y(y+9)-(3(y+9))=0

We multiply parentheses

5y^2+45y-(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

5y^2+45y-3y-27=0

We add all the numbers together, and all the variables

5y^2+42y-27=0

a = 5; b = 42; c = -27;
Δ = b2-4ac
Δ = 422-4·5·(-27)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-48}{2*5}=\frac{-90}{10}
=-9
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+48}{2*5}=\frac{6}{10}
=3/5
$