x^2/3=10.5

Solution for x^2/3=10.5 equation:

x^2/3=10.5

We move all terms to the left:

x^2/3-(10.5)=0

We add all the numbers together, and all the variables

x^2/3-10.5=0

We multiply all the terms by the denominator


x^2-(10.5)*3=0

We add all the numbers together, and all the variables

x^2-31.5=0

a = 1; b = 0; c = -31.5;
Δ = b2-4ac
Δ = 02-4·1·(-31.5)
Δ = 126
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:

$\sqrt{\Delta}=\sqrt{126}=\sqrt{9*14}=\sqrt{9}*\sqrt{14}=3\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-3\sqrt{14}}{2*1}=\frac{0-3\sqrt{14}}{2}
=-\frac{3\sqrt{14}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+3\sqrt{14}}{2*1}=\frac{0+3\sqrt{14}}{2}
=\frac{3\sqrt{14}}{2}
$