3/4x=8/x-1

Solution for 3/4x=8/x-1 equation:

3/4x=8/x-1

We move all terms to the left:

3/4x-(8/x-1)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: x-1)!=0

x∈R


We get rid of parentheses

3/4x-8/x+1=0

We calculate fractions


3x/4x^2+(-32x)/4x^2+1=0

We multiply all the terms by the denominator


3x+(-32x)+1*4x^2=0

Wy multiply elements

4x^2+3x+(-32x)=0

We get rid of parentheses

4x^2+3x-32x=0

We add all the numbers together, and all the variables

4x^2-29x=0

a = 4; b = -29; c = 0;
Δ = b2-4ac
Δ = -292-4·4·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-29}{2*4}=\frac{0}{8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+29}{2*4}=\frac{58}{8}
=7+1/4
$