3-1/4x=5/x

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

3-1/4x=5/x

We move all terms to the left:

3-1/4x-(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

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

We get rid of parentheses

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

We calculate fractions


(-x)/4x^2+(-20x)/4x^2+3=0

We add all the numbers together, and all the variables

(-1x)/4x^2+(-20x)/4x^2+3=0

We multiply all the terms by the denominator


(-1x)+(-20x)+3*4x^2=0

Wy multiply elements

12x^2+(-1x)+(-20x)=0

We get rid of parentheses

12x^2-1x-20x=0

We add all the numbers together, and all the variables

12x^2-21x=0

a = 12; b = -21; c = 0;
Δ = b2-4ac
Δ = -212-4·12·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-21}{2*12}=\frac{0}{24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+21}{2*12}=\frac{42}{24}
=1+3/4
$