36=1/2n+n

Solution for 36=1/2n+n equation:

36=1/2n+n

We move all terms to the left:

36-(1/2n+n)=0


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

n∈R


We add all the numbers together, and all the variables

-(+n+1/2n)+36=0

We get rid of parentheses

-n-1/2n+36=0

We multiply all the terms by the denominator


-n*2n+36*2n-1=0

Wy multiply elements

-2n^2+72n-1=0

a = -2; b = 72; c = -1;
Δ = b2-4ac
Δ = 722-4·(-2)·(-1)
Δ = 5176
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:

$\sqrt{\Delta}=\sqrt{5176}=\sqrt{4*1294}=\sqrt{4}*\sqrt{1294}=2\sqrt{1294}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-2\sqrt{1294}}{2*-2}=\frac{-72-2\sqrt{1294}}{-4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+2\sqrt{1294}}{2*-2}=\frac{-72+2\sqrt{1294}}{-4}
$