9/8x+3=3/x

Solution for 9/8x+3=3/x equation:

9/8x+3=3/x

We move all terms to the left:

9/8x+3-(3/x)=0


Domain of the equation: 8x!=0

x!=0/8

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

9/8x-(+3/x)+3=0

We get rid of parentheses

9/8x-3/x+3=0

We calculate fractions


9x/8x^2+(-24x)/8x^2+3=0

We multiply all the terms by the denominator


9x+(-24x)+3*8x^2=0

Wy multiply elements

24x^2+9x+(-24x)=0

We get rid of parentheses

24x^2+9x-24x=0

We add all the numbers together, and all the variables

24x^2-15x=0

a = 24; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·24·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*24}=\frac{0}{48}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*24}=\frac{30}{48}
=5/8
$