n-5/n=-7

Solution for n-5/n=-7 equation:

n-5/n=-7

We move all terms to the left:

n-5/n-(-7)=0


Domain of the equation: n!=0

n∈R


We add all the numbers together, and all the variables

n-5/n+7=0

We multiply all the terms by the denominator


n*n+7*n-5=0

We add all the numbers together, and all the variables

7n+n*n-5=0

Wy multiply elements

n^2+7n-5=0

a = 1; b = 7; c = -5;
Δ = b2-4ac
Δ = 72-4·1·(-5)
Δ = 69
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{69}}{2*1}=\frac{-7-\sqrt{69}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{69}}{2*1}=\frac{-7+\sqrt{69}}{2}
$