2/x=1/8x+3

Solution for 2/x=1/8x+3 equation:

2/x=1/8x+3

We move all terms to the left:

2/x-(1/8x+3)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 8x+3)!=0

x∈R


We get rid of parentheses

2/x-1/8x-3=0

We calculate fractions


16x/8x^2+(-x)/8x^2-3=0

We add all the numbers together, and all the variables

16x/8x^2+(-1x)/8x^2-3=0

We multiply all the terms by the denominator


16x+(-1x)-3*8x^2=0

Wy multiply elements

-24x^2+16x+(-1x)=0

We get rid of parentheses

-24x^2+16x-1x=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{-30}{-48}
=5/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*-24}=\frac{0}{-48}
=0
$