5/2*n=98-n

Solution for 5/2*n=98-n equation:

5/2n=98-n

We move all terms to the left:

5/2n-(98-n)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We add all the numbers together, and all the variables

5/2n-(-1n+98)=0

We get rid of parentheses

5/2n+1n-98=0

We multiply all the terms by the denominator


1n*2n-98*2n+5=0

Wy multiply elements

2n^2-196n+5=0

a = 2; b = -196; c = +5;
Δ = b2-4ac
Δ = -1962-4·2·5
Δ = 38376
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:

$\sqrt{\Delta}=\sqrt{38376}=\sqrt{36*1066}=\sqrt{36}*\sqrt{1066}=6\sqrt{1066}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-196)-6\sqrt{1066}}{2*2}=\frac{196-6\sqrt{1066}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-196)+6\sqrt{1066}}{2*2}=\frac{196+6\sqrt{1066}}{4}
$