-5/6n-1=1/2n+5

Solution for -5/6n-1=1/2n+5 equation:

-5/6n-1=1/2n+5

We move all terms to the left:

-5/6n-1-(1/2n+5)=0


Domain of the equation: 6n!=0

n!=0/6

n!=0

n∈R



Domain of the equation: 2n+5)!=0

n∈R


We get rid of parentheses

-5/6n-1/2n-5-1=0

We calculate fractions


(-10n)/12n^2+(-6n)/12n^2-5-1=0

We add all the numbers together, and all the variables

(-10n)/12n^2+(-6n)/12n^2-6=0

We multiply all the terms by the denominator


(-10n)+(-6n)-6*12n^2=0

Wy multiply elements

-72n^2+(-10n)+(-6n)=0

We get rid of parentheses

-72n^2-10n-6n=0

We add all the numbers together, and all the variables

-72n^2-16n=0

a = -72; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·(-72)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16}{2*-72}=\frac{0}{-144}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*-72}=\frac{32}{-144}
=-2/9
$