0.5x+1/3x+8=x

Solution for 0.5x+1/3x+8=x equation:

0.5x+1/3x+8=x

We move all terms to the left:

0.5x+1/3x+8-(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

-0.5x+1/3x+8=0

We multiply all the terms by the denominator


-(0.5x)*3x+8*3x+1=0

We add all the numbers together, and all the variables

-(+0.5x)*3x+8*3x+1=0

We multiply parentheses

-0x^2+8*3x+1=0

Wy multiply elements

-0x^2+24x+1=0

We add all the numbers together, and all the variables

-1x^2+24x+1=0

a = -1; b = 24; c = +1;
Δ = b2-4ac
Δ = 242-4·(-1)·1
Δ = 580
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:

$\sqrt{\Delta}=\sqrt{580}=\sqrt{4*145}=\sqrt{4}*\sqrt{145}=2\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{145}}{2*-1}=\frac{-24-2\sqrt{145}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{145}}{2*-1}=\frac{-24+2\sqrt{145}}{-2}
$