3x=488/x

Solution for 3x=488/x equation:

3x=488/x

We move all terms to the left:

3x-(488/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3x-(+488/x)=0

We get rid of parentheses

3x-488/x=0

We multiply all the terms by the denominator


3x*x-488=0

Wy multiply elements

3x^2-488=0

a = 3; b = 0; c = -488;
Δ = b2-4ac
Δ = 02-4·3·(-488)
Δ = 5856
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5856}=\sqrt{16*366}=\sqrt{16}*\sqrt{366}=4\sqrt{366}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{366}}{2*3}=\frac{0-4\sqrt{366}}{6}
=-\frac{4\sqrt{366}}{6}
=-\frac{2\sqrt{366}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{366}}{2*3}=\frac{0+4\sqrt{366}}{6}
=\frac{4\sqrt{366}}{6}
=\frac{2\sqrt{366}}{3}
$