3/x=x/5x-18

Solution for 3/x=x/5x-18 equation:

3/x=x/5x-18

We move all terms to the left:

3/x-(x/5x-18)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 5x-18)!=0

x∈R


We get rid of parentheses

3/x-x/5x+18=0

We calculate fractions


(-1x^2)/5x^2+15x/5x^2+18=0

We multiply all the terms by the denominator


(-1x^2)+15x+18*5x^2=0

Wy multiply elements

(-1x^2)+90x^2+15x=0

We get rid of parentheses

-1x^2+90x^2+15x=0

We add all the numbers together, and all the variables

89x^2+15x=0

a = 89; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·89·0
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*89}=\frac{-30}{178}
=-15/89
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*89}=\frac{0}{178}
=0
$