(3)/(x)=(15)/(8x)+3

Solution for (3)/(x)=(15)/(8x)+3 equation:

(3)/(x)=(15)/(8x)+3

We move all terms to the left:

(3)/(x)-((15)/(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

3/x-15/8x-3=0

We calculate fractions


24x/8x^2+(-15x)/8x^2-3=0

We multiply all the terms by the denominator


24x+(-15x)-3*8x^2=0

Wy multiply elements

-24x^2+24x+(-15x)=0

We get rid of parentheses

-24x^2+24x-15x=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
$