X-1/3x=1000

Solution for X-1/3x=1000 equation:

X-1/3X=1000

We move all terms to the left:

X-1/3X-(1000)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We multiply all the terms by the denominator


X*3X-1000*3X-1=0

Wy multiply elements

3X^2-3000X-1=0

a = 3; b = -3000; c = -1;
Δ = b2-4ac
Δ = -30002-4·3·(-1)
Δ = 9000012
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:

$\sqrt{\Delta}=\sqrt{9000012}=\sqrt{4*2250003}=\sqrt{4}*\sqrt{2250003}=2\sqrt{2250003}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3000)-2\sqrt{2250003}}{2*3}=\frac{3000-2\sqrt{2250003}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3000)+2\sqrt{2250003}}{2*3}=\frac{3000+2\sqrt{2250003}}{6}
$