1/4y=2/5y+-1

Solution for 1/4y=2/5y+-1 equation:

1/4y=2/5y+-1

We move all terms to the left:

1/4y-(2/5y+-1)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R



Domain of the equation: 5y+-1)!=0

y∈R


We add all the numbers together, and all the variables

1/4y-(2/5y-1)=0

We get rid of parentheses

1/4y-2/5y+1=0

We calculate fractions


5y/20y^2+(-8y)/20y^2+1=0

We multiply all the terms by the denominator


5y+(-8y)+1*20y^2=0

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

20y^2-3y=0

a = 20; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·20·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*20}=\frac{0}{40}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*20}=\frac{6}{40}
=3/20
$