5/3x+48=x

Solution for 5/3x+48=x equation:

5/3x+48=x

We move all terms to the left:

5/3x+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

-1x+5/3x+48=0

We multiply all the terms by the denominator


-1x*3x+48*3x+5=0

Wy multiply elements

-3x^2+144x+5=0

a = -3; b = 144; c = +5;
Δ = b2-4ac
Δ = 1442-4·(-3)·5
Δ = 20796
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:

$\sqrt{\Delta}=\sqrt{20796}=\sqrt{4*5199}=\sqrt{4}*\sqrt{5199}=2\sqrt{5199}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-2\sqrt{5199}}{2*-3}=\frac{-144-2\sqrt{5199}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+2\sqrt{5199}}{2*-3}=\frac{-144+2\sqrt{5199}}{-6}
$