318+x=1/3x

Solution for 318+x=1/3x equation:

318+x=1/3x

We move all terms to the left:

318+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)+318=0

We get rid of parentheses

x-1/3x+318=0

We multiply all the terms by the denominator


x*3x+318*3x-1=0

Wy multiply elements

3x^2+954x-1=0

a = 3; b = 954; c = -1;
Δ = b2-4ac
Δ = 9542-4·3·(-1)
Δ = 910128
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:

$\sqrt{\Delta}=\sqrt{910128}=\sqrt{16*56883}=\sqrt{16}*\sqrt{56883}=4\sqrt{56883}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(954)-4\sqrt{56883}}{2*3}=\frac{-954-4\sqrt{56883}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(954)+4\sqrt{56883}}{2*3}=\frac{-954+4\sqrt{56883}}{6}
$