(1/6)x=2000

Solution for (1/6)x=2000 equation:

(1/6)x=2000

We move all terms to the left:

(1/6)x-(2000)=0


Domain of the equation: 6)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/6)x-2000=0

We multiply parentheses

x^2-2000=0

a = 1; b = 0; c = -2000;
Δ = b2-4ac
Δ = 02-4·1·(-2000)
Δ = 8000
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:

$\sqrt{\Delta}=\sqrt{8000}=\sqrt{1600*5}=\sqrt{1600}*\sqrt{5}=40\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{5}}{2*1}=\frac{0-40\sqrt{5}}{2}
=-\frac{40\sqrt{5}}{2}
=-20\sqrt{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{5}}{2*1}=\frac{0+40\sqrt{5}}{2}
=\frac{40\sqrt{5}}{2}
=20\sqrt{5}
$