-4/3n+5=3/4n-1

Solution for -4/3n+5=3/4n-1 equation:

-4/3n+5=3/4n-1

We move all terms to the left:

-4/3n+5-(3/4n-1)=0


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R



Domain of the equation: 4n-1)!=0

n∈R


We get rid of parentheses

-4/3n-3/4n+1+5=0

We calculate fractions


(-16n)/12n^2+(-9n)/12n^2+1+5=0

We add all the numbers together, and all the variables

(-16n)/12n^2+(-9n)/12n^2+6=0

We multiply all the terms by the denominator


(-16n)+(-9n)+6*12n^2=0

Wy multiply elements

72n^2+(-16n)+(-9n)=0

We get rid of parentheses

72n^2-16n-9n=0

We add all the numbers together, and all the variables

72n^2-25n=0

a = 72; b = -25; c = 0;
Δ = b2-4ac
Δ = -252-4·72·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-25}{2*72}=\frac{0}{144}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+25}{2*72}=\frac{50}{144}
=25/72
$