x=1/3x+2100

Solution for x=1/3x+2100 equation:

x=1/3x+2100

We move all terms to the left:

x-(1/3x+2100)=0


Domain of the equation: 3x+2100)!=0

x∈R


We get rid of parentheses

x-1/3x-2100=0

We multiply all the terms by the denominator


x*3x-2100*3x-1=0

Wy multiply elements

3x^2-6300x-1=0

a = 3; b = -6300; c = -1;
Δ = b2-4ac
Δ = -63002-4·3·(-1)
Δ = 39690012
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:

$\sqrt{\Delta}=\sqrt{39690012}=\sqrt{4*9922503}=\sqrt{4}*\sqrt{9922503}=2\sqrt{9922503}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6300)-2\sqrt{9922503}}{2*3}=\frac{6300-2\sqrt{9922503}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6300)+2\sqrt{9922503}}{2*3}=\frac{6300+2\sqrt{9922503}}{6}
$