1/x=3x/8x+3

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

1/x=3x/8x+3

We move all terms to the left:

1/x-(3x/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

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

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

-3x^2-24x^2+8x=0

We add all the numbers together, and all the variables

-27x^2+8x=0

a = -27; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-27)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-27}=\frac{-16}{-54}
=8/27
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-27}=\frac{0}{-54}
=0
$