X-1/3x=3500

Solution for X-1/3x=3500 equation:

X-1/3X=3500

We move all terms to the left:

X-1/3X-(3500)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We multiply all the terms by the denominator


X*3X-3500*3X-1=0

Wy multiply elements

3X^2-10500X-1=0

a = 3; b = -10500; c = -1;
Δ = b2-4ac
Δ = -105002-4·3·(-1)
Δ = 110250012
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:

$\sqrt{\Delta}=\sqrt{110250012}=\sqrt{4*27562503}=\sqrt{4}*\sqrt{27562503}=2\sqrt{27562503}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10500)-2\sqrt{27562503}}{2*3}=\frac{10500-2\sqrt{27562503}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10500)+2\sqrt{27562503}}{2*3}=\frac{10500+2\sqrt{27562503}}{6}
$