3x=900/x

Solution for 3x=900/x equation:

3x=900/x

We move all terms to the left:

3x-(900/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-(+900/x)=0

We get rid of parentheses

3x-900/x=0

We multiply all the terms by the denominator


3x*x-900=0

Wy multiply elements

3x^2-900=0

a = 3; b = 0; c = -900;
Δ = b2-4ac
Δ = 02-4·3·(-900)
Δ = 10800
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:

$\sqrt{\Delta}=\sqrt{10800}=\sqrt{3600*3}=\sqrt{3600}*\sqrt{3}=60\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-60\sqrt{3}}{2*3}=\frac{0-60\sqrt{3}}{6}
=-\frac{60\sqrt{3}}{6}
=-10\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+60\sqrt{3}}{2*3}=\frac{0+60\sqrt{3}}{6}
=\frac{60\sqrt{3}}{6}
=10\sqrt{3}
$