5y(4+2y)=2y

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

5y(4+2y)=2y

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We multiply parentheses

10y^2-2y+20y=0

We add all the numbers together, and all the variables

10y^2+18y=0

a = 10; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·10·0
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{-(18)-18}{2*10}=\frac{-36}{20}
=-1+4/5
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*10}=\frac{0}{20}
=0
$