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
$