x^2=800/6

Solution for x^2=800/6 equation:

x^2=800/6

We move all terms to the left:

x^2-(800/6)=0

We add all the numbers together, and all the variables

x^2-(+800/6)=0

We get rid of parentheses

x^2-800/6=0

We multiply all the terms by the denominator


x^2*6-800=0

Wy multiply elements

6x^2-800=0

a = 6; b = 0; c = -800;
Δ = b2-4ac
Δ = 02-4·6·(-800)
Δ = 19200
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:

$\sqrt{\Delta}=\sqrt{19200}=\sqrt{6400*3}=\sqrt{6400}*\sqrt{3}=80\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-80\sqrt{3}}{2*6}=\frac{0-80\sqrt{3}}{12}
=-\frac{80\sqrt{3}}{12}
=-\frac{20\sqrt{3}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+80\sqrt{3}}{2*6}=\frac{0+80\sqrt{3}}{12}
=\frac{80\sqrt{3}}{12}
=\frac{20\sqrt{3}}{3}
$