(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∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-2x+(2x+24)-2x*x=0

Wy multiply elements

-2x^2-2x+(2x+24)=0

We get rid of parentheses

-2x^2-2x+2x+24=0

We add all the numbers together, and all the variables

-2x^2+24=0

a = -2; b = 0; c = +24;
Δ = b2-4ac
Δ = 02-4·(-2)·24
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{3}}{2*-2}=\frac{0-8\sqrt{3}}{-4}
=-\frac{8\sqrt{3}}{-4}
=-\frac{2\sqrt{3}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{3}}{2*-2}=\frac{0+8\sqrt{3}}{-4}
=\frac{8\sqrt{3}}{-4}
=\frac{2\sqrt{3}}{-1}
$