3/2n+18=1n-3

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

3/2n+18=1n-3

We move all terms to the left:

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


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


-n*2n+3*2n+18*2n+3=0

Wy multiply elements

-2n^2+6n+36n+3=0

We add all the numbers together, and all the variables

-2n^2+42n+3=0

a = -2; b = 42; c = +3;
Δ = b2-4ac
Δ = 422-4·(-2)·3
Δ = 1788
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:

$\sqrt{\Delta}=\sqrt{1788}=\sqrt{4*447}=\sqrt{4}*\sqrt{447}=2\sqrt{447}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-2\sqrt{447}}{2*-2}=\frac{-42-2\sqrt{447}}{-4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+2\sqrt{447}}{2*-2}=\frac{-42+2\sqrt{447}}{-4}
$