21/4x-1=5/x

Solution for 21/4x-1=5/x equation:

21/4x-1=5/x

We move all terms to the left:

21/4x-1-(5/x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

21/4x-(+5/x)-1=0

We get rid of parentheses

21/4x-5/x-1=0

We calculate fractions


21x/4x^2+(-20x)/4x^2-1=0

We multiply all the terms by the denominator


21x+(-20x)-1*4x^2=0

Wy multiply elements

-4x^2+21x+(-20x)=0

We get rid of parentheses

-4x^2+21x-20x=0

We add all the numbers together, and all the variables

-4x^2+x=0

a = -4; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-4)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-4}=\frac{-2}{-8}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-4}=\frac{0}{-8}
=0
$