x-1/3x=3000

Solution for x-1/3x=3000 equation:

x-1/3x=3000

We move all terms to the left:

x-1/3x-(3000)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


x*3x-3000*3x-1=0

Wy multiply elements

3x^2-9000x-1=0

a = 3; b = -9000; c = -1;
Δ = b2-4ac
Δ = -90002-4·3·(-1)
Δ = 81000012
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:

$\sqrt{\Delta}=\sqrt{81000012}=\sqrt{4*20250003}=\sqrt{4}*\sqrt{20250003}=2\sqrt{20250003}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9000)-2\sqrt{20250003}}{2*3}=\frac{9000-2\sqrt{20250003}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9000)+2\sqrt{20250003}}{2*3}=\frac{9000+2\sqrt{20250003}}{6}
$