-1/3x+48=-2x+8

Solution for -1/3x+48=-2x+8 equation:

-1/3x+48=-2x+8

We move all terms to the left:

-1/3x+48-(-2x+8)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

-1/3x+2x-8+48=0

We multiply all the terms by the denominator


2x*3x-8*3x+48*3x-1=0

Wy multiply elements

6x^2-24x+144x-1=0

We add all the numbers together, and all the variables

6x^2+120x-1=0

a = 6; b = 120; c = -1;
Δ = b2-4ac
Δ = 1202-4·6·(-1)
Δ = 14424
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:

$\sqrt{\Delta}=\sqrt{14424}=\sqrt{4*3606}=\sqrt{4}*\sqrt{3606}=2\sqrt{3606}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-2\sqrt{3606}}{2*6}=\frac{-120-2\sqrt{3606}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+2\sqrt{3606}}{2*6}=\frac{-120+2\sqrt{3606}}{12}
$