x-1/3x-2/3x=1100

Solution for x-1/3x-2/3x=1100 equation:

x-1/3x-2/3x=1100

We move all terms to the left:

x-1/3x-2/3x-(1100)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


x*3x-1100*3x-1-2=0

We add all the numbers together, and all the variables

x*3x-1100*3x-3=0

Wy multiply elements

3x^2-3300x-3=0

a = 3; b = -3300; c = -3;
Δ = b2-4ac
Δ = -33002-4·3·(-3)
Δ = 10890036
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:

$\sqrt{\Delta}=\sqrt{10890036}=\sqrt{36*302501}=\sqrt{36}*\sqrt{302501}=6\sqrt{302501}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3300)-6\sqrt{302501}}{2*3}=\frac{3300-6\sqrt{302501}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3300)+6\sqrt{302501}}{2*3}=\frac{3300+6\sqrt{302501}}{6}
$