1/3x+2/3x=16-x

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Solution for 1/3x+2/3x=16-x equation:



1/3x+2/3x=16-x
We move all terms to the left:
1/3x+2/3x-(16-x)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
We add all the numbers together, and all the variables
1/3x+2/3x-(-1x+16)=0
We get rid of parentheses
1/3x+2/3x+1x-16=0
We multiply all the terms by the denominator
1x*3x-16*3x+1+2=0
We add all the numbers together, and all the variables
1x*3x-16*3x+3=0
Wy multiply elements
3x^2-48x+3=0
a = 3; b = -48; c = +3;
Δ = b2-4ac
Δ = -482-4·3·3
Δ = 2268
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:
$\sqrt{\Delta}=\sqrt{2268}=\sqrt{324*7}=\sqrt{324}*\sqrt{7}=18\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-18\sqrt{7}}{2*3}=\frac{48-18\sqrt{7}}{6} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+18\sqrt{7}}{2*3}=\frac{48+18\sqrt{7}}{6} $

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