600-3/4n=3n

Solution for 600-3/4n=3n equation:

600-3/4n=3n

We move all terms to the left:

600-3/4n-(3n)=0


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R


We add all the numbers together, and all the variables

-3n-3/4n+600=0

We multiply all the terms by the denominator


-3n*4n+600*4n-3=0

Wy multiply elements

-12n^2+2400n-3=0

a = -12; b = 2400; c = -3;
Δ = b2-4ac
Δ = 24002-4·(-12)·(-3)
Δ = 5759856
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:

$\sqrt{\Delta}=\sqrt{5759856}=\sqrt{144*39999}=\sqrt{144}*\sqrt{39999}=12\sqrt{39999}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2400)-12\sqrt{39999}}{2*-12}=\frac{-2400-12\sqrt{39999}}{-24}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2400)+12\sqrt{39999}}{2*-12}=\frac{-2400+12\sqrt{39999}}{-24}
$