3/4x+5=3/x-9

Solution for 3/4x+5=3/x-9 equation:

3/4x+5=3/x-9

We move all terms to the left:

3/4x+5-(3/x-9)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: x-9)!=0

x∈R


We get rid of parentheses

3/4x-3/x+9+5=0

We calculate fractions


3x/4x^2+(-12x)/4x^2+9+5=0

We add all the numbers together, and all the variables

3x/4x^2+(-12x)/4x^2+14=0

We multiply all the terms by the denominator


3x+(-12x)+14*4x^2=0

Wy multiply elements

56x^2+3x+(-12x)=0

We get rid of parentheses

56x^2+3x-12x=0

We add all the numbers together, and all the variables

56x^2-9x=0

a = 56; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·56·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*56}=\frac{0}{112}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*56}=\frac{18}{112}
=9/56
$