5y(y+2)=3(y+2)

Solution for 5y(y+2)=3(y+2) equation:

5y(y+2)=3(y+2)

We move all terms to the left:

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

We multiply parentheses

5y^2+10y-(3(y+2))=0


We calculate terms in parentheses: -(3(y+2)), so:

3(y+2)

We multiply parentheses

3y+6

Back to the equation:

-(3y+6)


We get rid of parentheses

5y^2+10y-3y-6=0

We add all the numbers together, and all the variables

5y^2+7y-6=0

a = 5; b = 7; c = -6;
Δ = b2-4ac
Δ = 72-4·5·(-6)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-13}{2*5}=\frac{-20}{10}
=-2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+13}{2*5}=\frac{6}{10}
=3/5
$