5y(y+4)=2(y+4)

Solution for 5y(y+4)=2(y+4) equation:

5y(y+4)=2(y+4)

We move all terms to the left:

5y(y+4)-(2(y+4))=0

We multiply parentheses

5y^2+20y-(2(y+4))=0


We calculate terms in parentheses: -(2(y+4)), so:

2(y+4)

We multiply parentheses

2y+8

Back to the equation:

-(2y+8)


We get rid of parentheses

5y^2+20y-2y-8=0

We add all the numbers together, and all the variables

5y^2+18y-8=0

a = 5; b = 18; c = -8;
Δ = b2-4ac
Δ = 182-4·5·(-8)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-22}{2*5}=\frac{-40}{10}
=-4
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+22}{2*5}=\frac{4}{10}
=2/5
$