-4n-2/n=7

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

-4n-2/n=7

We move all terms to the left:

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


Domain of the equation: n!=0

n∈R


We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

a = -4; b = -7; c = -2;
Δ = b2-4ac
Δ = -72-4·(-4)·(-2)
Δ = 17
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{17}}{2*-4}=\frac{7-\sqrt{17}}{-8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{17}}{2*-4}=\frac{7+\sqrt{17}}{-8}
$