X+8=1/3x

Solution for X+8=1/3x equation:

X+8=1/3X

We move all terms to the left:

X+8-(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)+8=0

We get rid of parentheses

X-1/3X+8=0

We multiply all the terms by the denominator


X*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}
$