(24+2x/x)-1=2x+3/3

Solution for (24+2x/x)-1=2x+3/3 equation:

(24+2x/x)-1=2x+3/3

We move all terms to the left:

(24+2x/x)-1-(2x+3/3)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(2x/x+24)-(2x+1)-1=0

We get rid of parentheses

2x/x-2x+24-1-1=0

We multiply all the terms by the denominator


2x-2x*x+24*x-1*x-1*x=0

We add all the numbers together, and all the variables

24x-2x*x=0

Wy multiply elements

-2x^2+24x=0

a = -2; b = 24; c = 0;
Δ = b2-4ac
Δ = 242-4·(-2)·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24}{2*-2}=\frac{-48}{-4}
=+12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24}{2*-2}=\frac{0}{-4}
=0
$