576/2l+2l=68

Solution for 576/2l+2l=68 equation:

576/2l+2l=68

We move all terms to the left:

576/2l+2l-(68)=0


Domain of the equation: 2l!=0

l!=0/2

l!=0

l∈R


We add all the numbers together, and all the variables

2l+576/2l-68=0

We multiply all the terms by the denominator


2l*2l-68*2l+576=0

Wy multiply elements

4l^2-136l+576=0

a = 4; b = -136; c = +576;
Δ = b2-4ac
Δ = -1362-4·4·576
Δ = 9280
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:

$\sqrt{\Delta}=\sqrt{9280}=\sqrt{64*145}=\sqrt{64}*\sqrt{145}=8\sqrt{145}$
$l_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-136)-8\sqrt{145}}{2*4}=\frac{136-8\sqrt{145}}{8}
$
$l_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-136)+8\sqrt{145}}{2*4}=\frac{136+8\sqrt{145}}{8}
$