3/x=3+21/8x

Solution for 3/x=3+21/8x equation:

3/x=3+21/8x

We move all terms to the left:

3/x-(3+21/8x)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 8x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3/x-(21/8x+3)=0

We get rid of parentheses

3/x-21/8x-3=0

We calculate fractions


24x/8x^2+(-21x)/8x^2-3=0

We multiply all the terms by the denominator


24x+(-21x)-3*8x^2=0

Wy multiply elements

-24x^2+24x+(-21x)=0

We get rid of parentheses

-24x^2+24x-21x=0

We add all the numbers together, and all the variables

-24x^2+3x=0

a = -24; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-24)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-24}=\frac{-6}{-48}
=1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-24}=\frac{0}{-48}
=0
$