x=1/3x+5500

Solution for x=1/3x+5500 equation:

x=1/3x+5500

We move all terms to the left:

x-(1/3x+5500)=0


Domain of the equation: 3x+5500)!=0

x∈R


We get rid of parentheses

x-1/3x-5500=0

We multiply all the terms by the denominator


x*3x-5500*3x-1=0

Wy multiply elements

3x^2-16500x-1=0

a = 3; b = -16500; c = -1;
Δ = b2-4ac
Δ = -165002-4·3·(-1)
Δ = 272250012
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:

$\sqrt{\Delta}=\sqrt{272250012}=\sqrt{4*68062503}=\sqrt{4}*\sqrt{68062503}=2\sqrt{68062503}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16500)-2\sqrt{68062503}}{2*3}=\frac{16500-2\sqrt{68062503}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16500)+2\sqrt{68062503}}{2*3}=\frac{16500+2\sqrt{68062503}}{6}
$