2x+1/2x+2=24

Solution for 2x+1/2x+2=24 equation:

2x+1/2x+2=24

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

2x+1/2x-22=0

We multiply all the terms by the denominator


2x*2x-22*2x+1=0

Wy multiply elements

4x^2-44x+1=0

a = 4; b = -44; c = +1;
Δ = b2-4ac
Δ = -442-4·4·1
Δ = 1920
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:

$\sqrt{\Delta}=\sqrt{1920}=\sqrt{64*30}=\sqrt{64}*\sqrt{30}=8\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-8\sqrt{30}}{2*4}=\frac{44-8\sqrt{30}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+8\sqrt{30}}{2*4}=\frac{44+8\sqrt{30}}{8}
$