-n-1=-6-7/2n

Solution for -n-1=-6-7/2n equation:

-n-1=-6-7/2n

We move all terms to the left:

-n-1-(-6-7/2n)=0


Domain of the equation: 2n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

-n-(-7/2n-6)-1=0

We add all the numbers together, and all the variables

-1n-(-7/2n-6)-1=0

We get rid of parentheses

-1n+7/2n+6-1=0

We multiply all the terms by the denominator


-1n*2n+6*2n-1*2n+7=0

Wy multiply elements

-2n^2+12n-2n+7=0

We add all the numbers together, and all the variables

-2n^2+10n+7=0

a = -2; b = 10; c = +7;
Δ = b2-4ac
Δ = 102-4·(-2)·7
Δ = 156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{39}}{2*-2}=\frac{-10-2\sqrt{39}}{-4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{39}}{2*-2}=\frac{-10+2\sqrt{39}}{-4}
$