3x=288/x

Solution for 3x=288/x equation:

3x=288/x

We move all terms to the left:

3x-(288/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-(+288/x)=0

We get rid of parentheses

3x-288/x=0

We multiply all the terms by the denominator


3x*x-288=0

Wy multiply elements

3x^2-288=0

a = 3; b = 0; c = -288;
Δ = b2-4ac
Δ = 02-4·3·(-288)
Δ = 3456
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:

$\sqrt{\Delta}=\sqrt{3456}=\sqrt{576*6}=\sqrt{576}*\sqrt{6}=24\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{6}}{2*3}=\frac{0-24\sqrt{6}}{6}
=-\frac{24\sqrt{6}}{6}
=-4\sqrt{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{6}}{2*3}=\frac{0+24\sqrt{6}}{6}
=\frac{24\sqrt{6}}{6}
=4\sqrt{6}
$