1/9n+3/2n=4

Solution for 1/9n+3/2n=4 equation:

1/9n+3/2n=4

We move all terms to the left:

1/9n+3/2n-(4)=0


Domain of the equation: 9n!=0

n!=0/9

n!=0

n∈R



Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We calculate fractions


2n/18n^2+27n/18n^2-4=0

We multiply all the terms by the denominator


2n+27n-4*18n^2=0

We add all the numbers together, and all the variables

29n-4*18n^2=0

Wy multiply elements

-72n^2+29n=0

a = -72; b = 29; c = 0;
Δ = b2-4ac
Δ = 292-4·(-72)·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-29}{2*-72}=\frac{-58}{-144}
=29/72
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+29}{2*-72}=\frac{0}{-144}
=0
$