x^2/3=361

Solution for x^2/3=361 equation:

x^2/3=361

We move all terms to the left:

x^2/3-(361)=0

We multiply all the terms by the denominator


x^2-361*3=0

We add all the numbers together, and all the variables

x^2-1083=0

a = 1; b = 0; c = -1083;
Δ = b2-4ac
Δ = 02-4·1·(-1083)
Δ = 4332
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:

$\sqrt{\Delta}=\sqrt{4332}=\sqrt{1444*3}=\sqrt{1444}*\sqrt{3}=38\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-38\sqrt{3}}{2*1}=\frac{0-38\sqrt{3}}{2}
=-\frac{38\sqrt{3}}{2}
=-19\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+38\sqrt{3}}{2*1}=\frac{0+38\sqrt{3}}{2}
=\frac{38\sqrt{3}}{2}
=19\sqrt{3}
$