4/5n+2/3n=24

Solution for 4/5n+2/3n=24 equation:

4/5n+2/3n=24

We move all terms to the left:

4/5n+2/3n-(24)=0


Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R



Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R


We calculate fractions


12n/15n^2+10n/15n^2-24=0

We multiply all the terms by the denominator


12n+10n-24*15n^2=0

We add all the numbers together, and all the variables

22n-24*15n^2=0

Wy multiply elements

-360n^2+22n=0

a = -360; b = 22; c = 0;
Δ = b2-4ac
Δ = 222-4·(-360)·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-22}{2*-360}=\frac{-44}{-720}
=11/180
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+22}{2*-360}=\frac{0}{-720}
=0
$