3/4n+n=168

Solution for 3/4n+n=168 equation:

3/4n+n=168

We move all terms to the left:

3/4n+n-(168)=0


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R


We add all the numbers together, and all the variables

n+3/4n-168=0

We multiply all the terms by the denominator


n*4n-168*4n+3=0

Wy multiply elements

4n^2-672n+3=0

a = 4; b = -672; c = +3;
Δ = b2-4ac
Δ = -6722-4·4·3
Δ = 451536
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:

$\sqrt{\Delta}=\sqrt{451536}=\sqrt{16*28221}=\sqrt{16}*\sqrt{28221}=4\sqrt{28221}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-672)-4\sqrt{28221}}{2*4}=\frac{672-4\sqrt{28221}}{8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-672)+4\sqrt{28221}}{2*4}=\frac{672+4\sqrt{28221}}{8}
$