3/4n-7=-1/3n-5

Solution for 3/4n-7=-1/3n-5 equation:

3/4n-7=-1/3n-5

We move all terms to the left:

3/4n-7-(-1/3n-5)=0


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R



Domain of the equation: 3n-5)!=0

n∈R


We get rid of parentheses

3/4n+1/3n+5-7=0

We calculate fractions


9n/12n^2+4n/12n^2+5-7=0

We add all the numbers together, and all the variables

9n/12n^2+4n/12n^2-2=0

We multiply all the terms by the denominator


9n+4n-2*12n^2=0

We add all the numbers together, and all the variables

13n-2*12n^2=0

Wy multiply elements

-24n^2+13n=0

a = -24; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-24)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-24}=\frac{-26}{-48}
=13/24
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-24}=\frac{0}{-48}
=0
$