4/(x)=23/(8x)+3

Solution for 4/(x)=23/(8x)+3 equation:

4/(x)=23/(8x)+3

We move all terms to the left:

4/(x)-(23/(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

4/x-23/8x-3=0

We calculate fractions


32x/8x^2+(-23x)/8x^2-3=0

We multiply all the terms by the denominator


32x+(-23x)-3*8x^2=0

Wy multiply elements

-24x^2+32x+(-23x)=0

We get rid of parentheses

-24x^2+32x-23x=0

We add all the numbers together, and all the variables

-24x^2+9x=0

a = -24; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-24)·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*-24}=\frac{-18}{-48}
=3/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-24}=\frac{0}{-48}
=0
$