x^2/3=456

Solution for x^2/3=456 equation:

x^2/3=456

We move all terms to the left:

x^2/3-(456)=0

We multiply all the terms by the denominator


x^2-456*3=0

We add all the numbers together, and all the variables

x^2-1368=0

a = 1; b = 0; c = -1368;
Δ = b2-4ac
Δ = 02-4·1·(-1368)
Δ = 5472
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:

$\sqrt{\Delta}=\sqrt{5472}=\sqrt{144*38}=\sqrt{144}*\sqrt{38}=12\sqrt{38}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{38}}{2*1}=\frac{0-12\sqrt{38}}{2}
=-\frac{12\sqrt{38}}{2}
=-6\sqrt{38}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{38}}{2*1}=\frac{0+12\sqrt{38}}{2}
=\frac{12\sqrt{38}}{2}
=6\sqrt{38}
$