24=2l+1/2l+2

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

24=2l+1/2l+2

We move all terms to the left:

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


Domain of the equation: 2l+2)!=0

l∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-4l^2-4l+48l-1=0

We add all the numbers together, and all the variables

-4l^2+44l-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:
$l_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$l_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

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