24=2l+1/4l+1

Solution for 24=2l+1/4l+1 equation:

24=2l+1/4l+1

We move all terms to the left:

24-(2l+1/4l+1)=0


Domain of the equation: 4l+1)!=0

l∈R


We get rid of parentheses

-2l-1/4l-1+24=0

We multiply all the terms by the denominator


-2l*4l-1*4l+24*4l-1=0

Wy multiply elements

-8l^2-4l+96l-1=0

We add all the numbers together, and all the variables

-8l^2+92l-1=0

a = -8; b = 92; c = -1;
Δ = b2-4ac
Δ = 922-4·(-8)·(-1)
Δ = 8432
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:

$\sqrt{\Delta}=\sqrt{8432}=\sqrt{16*527}=\sqrt{16}*\sqrt{527}=4\sqrt{527}$
$l_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(92)-4\sqrt{527}}{2*-8}=\frac{-92-4\sqrt{527}}{-16}
$
$l_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(92)+4\sqrt{527}}{2*-8}=\frac{-92+4\sqrt{527}}{-16}
$