x-1/3x=499

Solution for x-1/3x=499 equation:

x-1/3x=499

We move all terms to the left:

x-1/3x-(499)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


x*3x-499*3x-1=0

Wy multiply elements

3x^2-1497x-1=0

a = 3; b = -1497; c = -1;
Δ = b2-4ac
Δ = -14972-4·3·(-1)
Δ = 2241021
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1497)-\sqrt{2241021}}{2*3}=\frac{1497-\sqrt{2241021}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1497)+\sqrt{2241021}}{2*3}=\frac{1497+\sqrt{2241021}}{6}
$