1/3x+5-x=9

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Solution for 1/3x+5-x=9 equation:



1/3x+5-x=9
We move all terms to the left:
1/3x+5-x-(9)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
We add all the numbers together, and all the variables
-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 = 156
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:
$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{39}}{2*-3}=\frac{12-2\sqrt{39}}{-6} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{39}}{2*-3}=\frac{12+2\sqrt{39}}{-6} $

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