(1/3x)x=300

Solution for (1/3x)x=300 equation:

(1/3x)x=300

We move all terms to the left:

(1/3x)x-(300)=0


Domain of the equation: 3x)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/3x)x-300=0

We multiply parentheses

x^2-300=0

a = 1; b = 0; c = -300;
Δ = b2-4ac
Δ = 02-4·1·(-300)
Δ = 1200
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:

$\sqrt{\Delta}=\sqrt{1200}=\sqrt{400*3}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{3}}{2*1}=\frac{0-20\sqrt{3}}{2}
=-\frac{20\sqrt{3}}{2}
=-10\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{3}}{2*1}=\frac{0+20\sqrt{3}}{2}
=\frac{20\sqrt{3}}{2}
=10\sqrt{3}
$