3/4n-18=1/2n-4

Solution for 3/4n-18=1/2n-4 equation:

3/4n-18=1/2n-4

We move all terms to the left:

3/4n-18-(1/2n-4)=0


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R



Domain of the equation: 2n-4)!=0

n∈R


We get rid of parentheses

3/4n-1/2n+4-18=0

We calculate fractions


6n/8n^2+(-4n)/8n^2+4-18=0

We add all the numbers together, and all the variables

6n/8n^2+(-4n)/8n^2-14=0

We multiply all the terms by the denominator


6n+(-4n)-14*8n^2=0

Wy multiply elements

-112n^2+6n+(-4n)=0

We get rid of parentheses

-112n^2+6n-4n=0

We add all the numbers together, and all the variables

-112n^2+2n=0

a = -112; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-112)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-112}=\frac{-4}{-224}
=1/56
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-112}=\frac{0}{-224}
=0
$