2+1/3l=1+1/4l

Solution for 2+1/3l=1+1/4l equation:

2+1/3l=1+1/4l

We move all terms to the left:

2+1/3l-(1+1/4l)=0


Domain of the equation: 3l!=0

l!=0/3

l!=0

l∈R



Domain of the equation: 4l)!=0

l!=0/1

l!=0

l∈R


We add all the numbers together, and all the variables

1/3l-(1/4l+1)+2=0

We get rid of parentheses

1/3l-1/4l-1+2=0

We calculate fractions


4l/12l^2+(-3l)/12l^2-1+2=0

We add all the numbers together, and all the variables

4l/12l^2+(-3l)/12l^2+1=0

We multiply all the terms by the denominator


4l+(-3l)+1*12l^2=0

Wy multiply elements

12l^2+4l+(-3l)=0

We get rid of parentheses

12l^2+4l-3l=0

We add all the numbers together, and all the variables

12l^2+l=0

a = 12; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·12·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$l_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$l_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$l_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*12}=\frac{-2}{24}
=-1/12
$
$l_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*12}=\frac{0}{24}
=0
$