3/4n=-5n-18

Solution for 3/4n=-5n-18 equation:

3/4n=-5n-18

We move all terms to the left:

3/4n-(-5n-18)=0


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R


We get rid of parentheses

3/4n+5n+18=0

We multiply all the terms by the denominator


5n*4n+18*4n+3=0

Wy multiply elements

20n^2+72n+3=0

a = 20; b = 72; c = +3;
Δ = b2-4ac
Δ = 722-4·20·3
Δ = 4944
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4944}=\sqrt{16*309}=\sqrt{16}*\sqrt{309}=4\sqrt{309}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-4\sqrt{309}}{2*20}=\frac{-72-4\sqrt{309}}{40}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+4\sqrt{309}}{2*20}=\frac{-72+4\sqrt{309}}{40}
$