5-2/7n=1/2n+13

Solution for 5-2/7n=1/2n+13 equation:

5-2/7n=1/2n+13

We move all terms to the left:

5-2/7n-(1/2n+13)=0


Domain of the equation: 7n!=0

n!=0/7

n!=0

n∈R



Domain of the equation: 2n+13)!=0

n∈R


We get rid of parentheses

-2/7n-1/2n-13+5=0

We calculate fractions


(-4n)/14n^2+(-7n)/14n^2-13+5=0

We add all the numbers together, and all the variables

(-4n)/14n^2+(-7n)/14n^2-8=0

We multiply all the terms by the denominator


(-4n)+(-7n)-8*14n^2=0

Wy multiply elements

-112n^2+(-4n)+(-7n)=0

We get rid of parentheses

-112n^2-4n-7n=0

We add all the numbers together, and all the variables

-112n^2-11n=0

a = -112; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·(-112)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-11}{2*-112}=\frac{0}{-224}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*-112}=\frac{22}{-224}
=-11/112
$