1/4y=2/5y-4

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

1/4y=2/5y-4

We move all terms to the left:

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


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R



Domain of the equation: 5y-4)!=0

y∈R


We get rid of parentheses

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

We calculate fractions


5y/20y^2+(-8y)/20y^2+4=0

We multiply all the terms by the denominator


5y+(-8y)+4*20y^2=0

Wy multiply elements

80y^2+5y+(-8y)=0

We get rid of parentheses

80y^2+5y-8y=0

We add all the numbers together, and all the variables

80y^2-3y=0

a = 80; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·80·0
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*80}=\frac{0}{160}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*80}=\frac{6}{160}
=3/80
$