2/3l+1/5l=13/15

Solution for 2/3l+1/5l=13/15 equation:

2/3l+1/5l=13/15

We move all terms to the left:

2/3l+1/5l-(13/15)=0


Domain of the equation: 3l!=0

l!=0/3

l!=0

l∈R



Domain of the equation: 5l!=0

l!=0/5

l!=0

l∈R


We add all the numbers together, and all the variables

2/3l+1/5l-(+13/15)=0

We get rid of parentheses

2/3l+1/5l-13/15=0

We calculate fractions


(-975l^2)/225l^2+150l/225l^2+45l/225l^2=0

We multiply all the terms by the denominator


(-975l^2)+150l+45l=0

We add all the numbers together, and all the variables

(-975l^2)+195l=0

We get rid of parentheses

-975l^2+195l=0

a = -975; b = 195; c = 0;
Δ = b2-4ac
Δ = 1952-4·(-975)·0
Δ = 38025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$l_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$l_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{38025}=195$
$l_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(195)-195}{2*-975}=\frac{-390}{-1950}
=1/5
$
$l_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(195)+195}{2*-975}=\frac{0}{-1950}
=0
$