3/x=9/8x+20

Solution for 3/x=9/8x+20 equation:

3/x=9/8x+20

We move all terms to the left:

3/x-(9/8x+20)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 8x+20)!=0

x∈R


We get rid of parentheses

3/x-9/8x-20=0

We calculate fractions


24x/8x^2+(-9x)/8x^2-20=0

We multiply all the terms by the denominator


24x+(-9x)-20*8x^2=0

Wy multiply elements

-160x^2+24x+(-9x)=0

We get rid of parentheses

-160x^2+24x-9x=0

We add all the numbers together, and all the variables

-160x^2+15x=0

a = -160; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·(-160)·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*-160}=\frac{-30}{-320}
=3/32
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*-160}=\frac{0}{-320}
=0
$