(-2000/x^2)+3=0

Solution for (-2000/x^2)+3=0 equation:

(-2000/x^2)+3=0


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

x!=0/1

x!=0

x∈R


We get rid of parentheses

-2000/x^2+3=0

We multiply all the terms by the denominator


3*x^2-2000=0

We add all the numbers together, and all the variables

3x^2-2000=0

a = 3; b = 0; c = -2000;
Δ = b2-4ac
Δ = 02-4·3·(-2000)
Δ = 24000
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:

$\sqrt{\Delta}=\sqrt{24000}=\sqrt{1600*15}=\sqrt{1600}*\sqrt{15}=40\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{15}}{2*3}=\frac{0-40\sqrt{15}}{6}
=-\frac{40\sqrt{15}}{6}
=-\frac{20\sqrt{15}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{15}}{2*3}=\frac{0+40\sqrt{15}}{6}
=\frac{40\sqrt{15}}{6}
=\frac{20\sqrt{15}}{3}
$