71/3=x2

Solution for 71/3=x2 equation:

71/3=x2

We move all terms to the left:

71/3-(x2)=0

We add all the numbers together, and all the variables

-1x^2+71/3=0

We multiply all the terms by the denominator


-1x^2*3+71=0

Wy multiply elements

-3x^2+71=0

a = -3; b = 0; c = +71;
Δ = b2-4ac
Δ = 02-4·(-3)·71
Δ = 852
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:

$\sqrt{\Delta}=\sqrt{852}=\sqrt{4*213}=\sqrt{4}*\sqrt{213}=2\sqrt{213}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{213}}{2*-3}=\frac{0-2\sqrt{213}}{-6}
=-\frac{2\sqrt{213}}{-6}
=-\frac{\sqrt{213}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{213}}{2*-3}=\frac{0+2\sqrt{213}}{-6}
=\frac{2\sqrt{213}}{-6}
=\frac{\sqrt{213}}{-3}
$