1/x-1/4=3/5x

Solution for 1/x-1/4=3/5x equation:

1/x-1/4=3/5x

We move all terms to the left:

1/x-1/4-(3/5x)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/x-(+3/5x)-1/4=0

We get rid of parentheses

1/x-3/5x-1/4=0

We calculate fractions


(-25x^2)/80x^2+80x/80x^2+(-48x)/80x^2=0

We multiply all the terms by the denominator


(-25x^2)+80x+(-48x)=0

We get rid of parentheses

-25x^2+80x-48x=0

We add all the numbers together, and all the variables

-25x^2+32x=0

a = -25; b = 32; c = 0;
Δ = b2-4ac
Δ = 322-4·(-25)·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-32}{2*-25}=\frac{-64}{-50}
=1+7/25
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+32}{2*-25}=\frac{0}{-50}
=0
$