4(3/4n-5)=3(2/3n-11)

Solution for 4(3/4n-5)=3(2/3n-11) equation:

4(3/4n-5)=3(2/3n-11)

We move all terms to the left:

4(3/4n-5)-(3(2/3n-11))=0


Domain of the equation: 4n-5)!=0

n∈R



Domain of the equation: 3n-11))!=0

n∈R


We multiply parentheses

12n-(3(2/3n-11))-20=0

We multiply all the terms by the denominator


12n*3n-20*3n-11))-(3(2-11))=0

We add all the numbers together, and all the variables

12n*3n-20*3n-11))-(3(-9))=0

We add all the numbers together, and all the variables

12n*3n-20*3n=0

Wy multiply elements

36n^2-60n=0

a = 36; b = -60; c = 0;
Δ = b2-4ac
Δ = -602-4·36·0
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-60}{2*36}=\frac{0}{72}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+60}{2*36}=\frac{120}{72}
=1+2/3
$