4/n+2=7n

Solution for 4/n+2=7n equation:

4/n+2=7n

We move all terms to the left:

4/n+2-(7n)=0


Domain of the equation: n!=0

n∈R


We add all the numbers together, and all the variables

-7n+4/n+2=0

We multiply all the terms by the denominator


-7n*n+2*n+4=0

We add all the numbers together, and all the variables

2n-7n*n+4=0

Wy multiply elements

-7n^2+2n+4=0

a = -7; b = 2; c = +4;
Δ = b2-4ac
Δ = 22-4·(-7)·4
Δ = 116
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:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{29}}{2*-7}=\frac{-2-2\sqrt{29}}{-14}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{29}}{2*-7}=\frac{-2+2\sqrt{29}}{-14}
$