1/2n-4=2n-37

Solution for 1/2n-4=2n-37 equation:

1/2n-4=2n-37

We move all terms to the left:

1/2n-4-(2n-37)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We get rid of parentheses

1/2n-2n+37-4=0

We multiply all the terms by the denominator


-2n*2n+37*2n-4*2n+1=0

Wy multiply elements

-4n^2+74n-8n+1=0

We add all the numbers together, and all the variables

-4n^2+66n+1=0

a = -4; b = 66; c = +1;
Δ = b2-4ac
Δ = 662-4·(-4)·1
Δ = 4372
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:

$\sqrt{\Delta}=\sqrt{4372}=\sqrt{4*1093}=\sqrt{4}*\sqrt{1093}=2\sqrt{1093}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(66)-2\sqrt{1093}}{2*-4}=\frac{-66-2\sqrt{1093}}{-8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(66)+2\sqrt{1093}}{2*-4}=\frac{-66+2\sqrt{1093}}{-8}
$