2/5y-2/25=5/2y

Solution for 2/5y-2/25=5/2y equation:

2/5y-2/25=5/2y

We move all terms to the left:

2/5y-2/25-(5/2y)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R



Domain of the equation: 2y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

2/5y-(+5/2y)-2/25=0

We get rid of parentheses

2/5y-5/2y-2/25=0

We calculate fractions


(-40y^2)/500y^2+200y/500y^2+(-1250y)/500y^2=0

We multiply all the terms by the denominator


(-40y^2)+200y+(-1250y)=0

We get rid of parentheses

-40y^2+200y-1250y=0

We add all the numbers together, and all the variables

-40y^2-1050y=0

a = -40; b = -1050; c = 0;
Δ = b2-4ac
Δ = -10502-4·(-40)·0
Δ = 1102500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1102500}=1050$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1050)-1050}{2*-40}=\frac{0}{-80}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1050)+1050}{2*-40}=\frac{2100}{-80}
=-26+1/4
$