3/x=15/8x+13

Solution for 3/x=15/8x+13 equation:

3/x=15/8x+13

We move all terms to the left:

3/x-(15/8x+13)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 8x+13)!=0

x∈R


We get rid of parentheses

3/x-15/8x-13=0

We calculate fractions


24x/8x^2+(-15x)/8x^2-13=0

We multiply all the terms by the denominator


24x+(-15x)-13*8x^2=0

Wy multiply elements

-104x^2+24x+(-15x)=0

We get rid of parentheses

-104x^2+24x-15x=0

We add all the numbers together, and all the variables

-104x^2+9x=0

a = -104; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-104)·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*-104}=\frac{-18}{-208}
=9/104
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-104}=\frac{0}{-208}
=0
$