-1/3x+24=-x+8

Solution for -1/3x+24=-x+8 equation:

-1/3x+24=-x+8

We move all terms to the left:

-1/3x+24-(-x+8)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-1/3x-(-1x+8)+24=0

We get rid of parentheses

-1/3x+1x-8+24=0

We multiply all the terms by the denominator


1x*3x-8*3x+24*3x-1=0

Wy multiply elements

3x^2-24x+72x-1=0

We add all the numbers together, and all the variables

3x^2+48x-1=0

a = 3; b = 48; c = -1;
Δ = b2-4ac
Δ = 482-4·3·(-1)
Δ = 2316
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:

$\sqrt{\Delta}=\sqrt{2316}=\sqrt{4*579}=\sqrt{4}*\sqrt{579}=2\sqrt{579}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-2\sqrt{579}}{2*3}=\frac{-48-2\sqrt{579}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+2\sqrt{579}}{2*3}=\frac{-48+2\sqrt{579}}{6}
$