48-1/3x=x

Solution for 48-1/3x=x equation:

48-1/3x=x

We move all terms to the left:

48-1/3x-(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

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

We multiply all the terms by the denominator


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

Wy multiply elements

-3x^2+144x-1=0

a = -3; b = 144; c = -1;
Δ = b2-4ac
Δ = 1442-4·(-3)·(-1)
Δ = 20724
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:

$\sqrt{\Delta}=\sqrt{20724}=\sqrt{4*5181}=\sqrt{4}*\sqrt{5181}=2\sqrt{5181}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-2\sqrt{5181}}{2*-3}=\frac{-144-2\sqrt{5181}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+2\sqrt{5181}}{2*-3}=\frac{-144+2\sqrt{5181}}{-6}
$