1/3x=48-x

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

1/3x=48-x

We move all terms to the left:

1/3x-(48-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

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

We get rid of parentheses

1/3x+1x-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}
$