/2n+2=n+10

Solution for /2n+2=n+10 equation:

/2n+2=n+10

We move all terms to the left:

/2n+2-(n+10)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We get rid of parentheses

/2n-n-10+2=0

We multiply all the terms by the denominator


-n*2n-10*2n+2*2n+=0

We add all the numbers together, and all the variables

-n*2n-10*2n+2*2n=0

Wy multiply elements

-2n^2-20n+4n=0

We add all the numbers together, and all the variables

-2n^2-16n=0

a = -2; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·(-2)·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*-2}=\frac{0}{-4}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*-2}=\frac{32}{-4}
=-8
$