n=9/n+7=4/3

Solution for n=9/n+7=4/3 equation:

n=9/n+7=4/3

We move all terms to the left:

n-(9/n+7)=0


Domain of the equation: n+7)!=0

n∈R


We get rid of parentheses

n-9/n-7=0

We multiply all the terms by the denominator


n*n-7*n-9=0

We add all the numbers together, and all the variables

-7n+n*n-9=0

Wy multiply elements

n^2-7n-9=0

a = 1; b = -7; c = -9;
Δ = b2-4ac
Δ = -72-4·1·(-9)
Δ = 85
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{85}}{2*1}=\frac{7-\sqrt{85}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{85}}{2*1}=\frac{7+\sqrt{85}}{2}
$