5/x-4=3/4x

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

5/x-4=3/4x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

-16x^2+20x+(-3x)=0

We get rid of parentheses

-16x^2+20x-3x=0

We add all the numbers together, and all the variables

-16x^2+17x=0

a = -16; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-16)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*-16}=\frac{-34}{-32}
=1+1/16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-16}=\frac{0}{-32}
=0
$