2x=4/2x+24

Solution for 2x=4/2x+24 equation:

2x=4/2x+24

We move all terms to the left:

2x-(4/2x+24)=0


Domain of the equation: 2x+24)!=0

x∈R


We get rid of parentheses

2x-4/2x-24=0

We multiply all the terms by the denominator


2x*2x-24*2x-4=0

Wy multiply elements

4x^2-48x-4=0

a = 4; b = -48; c = -4;
Δ = b2-4ac
Δ = -482-4·4·(-4)
Δ = 2368
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:

$\sqrt{\Delta}=\sqrt{2368}=\sqrt{64*37}=\sqrt{64}*\sqrt{37}=8\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-8\sqrt{37}}{2*4}=\frac{48-8\sqrt{37}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+8\sqrt{37}}{2*4}=\frac{48+8\sqrt{37}}{8}
$