n-5/3n+3=0

Solution for n-5/3n+3=0 equation:

n-5/3n+3=0


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R


We multiply all the terms by the denominator


n*3n+3*3n-5=0

Wy multiply elements

3n^2+9n-5=0

a = 3; b = 9; c = -5;
Δ = b2-4ac
Δ = 92-4·3·(-5)
Δ = 141
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{-(9)-\sqrt{141}}{2*3}=\frac{-9-\sqrt{141}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{141}}{2*3}=\frac{-9+\sqrt{141}}{6}
$