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

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

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

We move all terms to the left:

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

We multiply parentheses

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


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

2(y+3)

We multiply parentheses

2y+6

Back to the equation:

-(2y+6)


We get rid of parentheses

5y^2+15y-2y-6=0

We add all the numbers together, and all the variables

5y^2+13y-6=0

a = 5; b = 13; c = -6;
Δ = b2-4ac
Δ = 132-4·5·(-6)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-17}{2*5}=\frac{-30}{10}
=-3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+17}{2*5}=\frac{4}{10}
=2/5
$