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1/3x+4+380=x
We move all terms to the left:
1/3x+4+380-(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+384=0
We multiply all the terms by the denominator
-1x*3x+384*3x+1=0
Wy multiply elements
-3x^2+1152x+1=0
a = -3; b = 1152; c = +1;
Δ = b2-4ac
Δ = 11522-4·(-3)·1
Δ = 1327116
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1327116}=\sqrt{196*6771}=\sqrt{196}*\sqrt{6771}=14\sqrt{6771}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1152)-14\sqrt{6771}}{2*-3}=\frac{-1152-14\sqrt{6771}}{-6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1152)+14\sqrt{6771}}{2*-3}=\frac{-1152+14\sqrt{6771}}{-6} $
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