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

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

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

We move all terms to the left:

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


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R



Domain of the equation: 4n-18)!=0

n∈R


We get rid of parentheses

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

We calculate fractions


4n/8n^2+6n/8n^2+18+4=0

We add all the numbers together, and all the variables

4n/8n^2+6n/8n^2+22=0

We multiply all the terms by the denominator


4n+6n+22*8n^2=0

We add all the numbers together, and all the variables

10n+22*8n^2=0

Wy multiply elements

176n^2+10n=0

a = 176; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·176·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*176}=\frac{-20}{352}
=-5/88
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*176}=\frac{0}{352}
=0
$