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

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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} $

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