1/3x+4+380=x

Solution for 1/3x+4+380=x equation:

1/3x+4+380=x

We move all terms to the left:

1/3x+4+380-(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

-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}
$