X+11/3x+11/3x-1=43

Solution for X+11/3x+11/3x-1=43 equation:

X+11/3X+11/3X-1=43

We move all terms to the left:

X+11/3X+11/3X-1-(43)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We add all the numbers together, and all the variables

X+11/3X+11/3X-44=0

We multiply all the terms by the denominator


X*3X-44*3X+11+11=0

We add all the numbers together, and all the variables

X*3X-44*3X+22=0

Wy multiply elements

3X^2-132X+22=0

a = 3; b = -132; c = +22;
Δ = b2-4ac
Δ = -1322-4·3·22
Δ = 17160
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:

$\sqrt{\Delta}=\sqrt{17160}=\sqrt{4*4290}=\sqrt{4}*\sqrt{4290}=2\sqrt{4290}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-132)-2\sqrt{4290}}{2*3}=\frac{132-2\sqrt{4290}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-132)+2\sqrt{4290}}{2*3}=\frac{132+2\sqrt{4290}}{6}
$