4-x=1/3x

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Solution for 4-x=1/3x equation:



4-x=1/3x
We move all terms to the left:
4-x-(1/3x)=0
Domain of the equation: 3x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
-x-(+1/3x)+4=0
We add all the numbers together, and all the variables
-1x-(+1/3x)+4=0
We get rid of parentheses
-1x-1/3x+4=0
We multiply all the terms by the denominator
-1x*3x+4*3x-1=0
Wy multiply elements
-3x^2+12x-1=0
a = -3; b = 12; c = -1;
Δ = b2-4ac
Δ = 122-4·(-3)·(-1)
Δ = 132
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:
$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{33}}{2*-3}=\frac{-12-2\sqrt{33}}{-6} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{33}}{2*-3}=\frac{-12+2\sqrt{33}}{-6} $

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