5/4(2l)+2l=24

Solution for 5/4(2l)+2l=24 equation:

5/4(2l)+2l=24

We move all terms to the left:

5/4(2l)+2l-(24)=0


Domain of the equation: 42l!=0

l!=0/42

l!=0

l∈R


We add all the numbers together, and all the variables

2l+5/42l-24=0

We multiply all the terms by the denominator


2l*42l-24*42l+5=0

Wy multiply elements

84l^2-1008l+5=0

a = 84; b = -1008; c = +5;
Δ = b2-4ac
Δ = -10082-4·84·5
Δ = 1014384
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:

$\sqrt{\Delta}=\sqrt{1014384}=\sqrt{16*63399}=\sqrt{16}*\sqrt{63399}=4\sqrt{63399}$
$l_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1008)-4\sqrt{63399}}{2*84}=\frac{1008-4\sqrt{63399}}{168}
$
$l_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1008)+4\sqrt{63399}}{2*84}=\frac{1008+4\sqrt{63399}}{168}
$