3/x=x/48x

Solution for 3/x=x/48x equation:

3/x=x/48x

We move all terms to the left:

3/x-(x/48x)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 48x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3/x-(+x/48x)=0

We get rid of parentheses

3/x-x/48x=0

We calculate fractions


(-1x^2)/48x^2+144x/48x^2=0

We multiply all the terms by the denominator


(-1x^2)+144x=0

We get rid of parentheses

-1x^2+144x=0

a = -1; b = 144; c = 0;
Δ = b2-4ac
Δ = 1442-4·(-1)·0
Δ = 20736
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{20736}=144$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-144}{2*-1}=\frac{-288}{-2}
=+144
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+144}{2*-1}=\frac{0}{-2}
=0
$