108=2l+54/l

Solution for 108=2l+54/l equation:

108=2l+54/l

We move all terms to the left:

108-(2l+54/l)=0


Domain of the equation: l)!=0

l!=0/1

l!=0

l∈R


We add all the numbers together, and all the variables

-(+2l+54/l)+108=0

We get rid of parentheses

-2l-54/l+108=0

We multiply all the terms by the denominator


-2l*l+108*l-54=0

We add all the numbers together, and all the variables

108l-2l*l-54=0

Wy multiply elements

-2l^2+108l-54=0

a = -2; b = 108; c = -54;
Δ = b2-4ac
Δ = 1082-4·(-2)·(-54)
Δ = 11232
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:

$\sqrt{\Delta}=\sqrt{11232}=\sqrt{144*78}=\sqrt{144}*\sqrt{78}=12\sqrt{78}$
$l_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(108)-12\sqrt{78}}{2*-2}=\frac{-108-12\sqrt{78}}{-4}
$
$l_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(108)+12\sqrt{78}}{2*-2}=\frac{-108+12\sqrt{78}}{-4}
$