2/5y=4y

Solution for 2/5y=4y equation:

2/5y=4y

We move all terms to the left:

2/5y-(4y)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R


We add all the numbers together, and all the variables

-4y+2/5y=0

We multiply all the terms by the denominator


-4y*5y+2=0

Wy multiply elements

-20y^2+2=0

a = -20; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-20)·2
Δ = 160
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{10}}{2*-20}=\frac{0-4\sqrt{10}}{-40}
=-\frac{4\sqrt{10}}{-40}
=-\frac{\sqrt{10}}{-10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{10}}{2*-20}=\frac{0+4\sqrt{10}}{-40}
=\frac{4\sqrt{10}}{-40}
=\frac{\sqrt{10}}{-10}
$