1000=20/6x^2

Solution for 1000=20/6x^2 equation:

1000=20/6x^2

We move all terms to the left:

1000-(20/6x^2)=0


Domain of the equation: 6x^2)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

-20/6x^2+1000=0

We multiply all the terms by the denominator


1000*6x^2-20=0

Wy multiply elements

6000x^2-20=0

a = 6000; b = 0; c = -20;
Δ = b2-4ac
Δ = 02-4·6000·(-20)
Δ = 480000
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:

$\sqrt{\Delta}=\sqrt{480000}=\sqrt{160000*3}=\sqrt{160000}*\sqrt{3}=400\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-400\sqrt{3}}{2*6000}=\frac{0-400\sqrt{3}}{12000}
=-\frac{400\sqrt{3}}{12000}
=-\frac{\sqrt{3}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+400\sqrt{3}}{2*6000}=\frac{0+400\sqrt{3}}{12000}
=\frac{400\sqrt{3}}{12000}
=\frac{\sqrt{3}}{30}
$