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1/3x-8=x
We move all terms to the left:
1/3x-8-(x)=0
Domain of the equation: 3x!=0We add all the numbers together, and all the variables
x!=0/3
x!=0
x∈R
-1x+1/3x-8=0
We multiply all the terms by the denominator
-1x*3x-8*3x+1=0
Wy multiply elements
-3x^2-24x+1=0
a = -3; b = -24; c = +1;
Δ = b2-4ac
Δ = -242-4·(-3)·1
Δ = 588
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{588}=\sqrt{196*3}=\sqrt{196}*\sqrt{3}=14\sqrt{3}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-14\sqrt{3}}{2*-3}=\frac{24-14\sqrt{3}}{-6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+14\sqrt{3}}{2*-3}=\frac{24+14\sqrt{3}}{-6} $
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