3n+20=1/2n-8

Solution for 3n+20=1/2n-8 equation:

3n+20=1/2n-8

We move all terms to the left:

3n+20-(1/2n-8)=0


Domain of the equation: 2n-8)!=0

n∈R


We get rid of parentheses

3n-1/2n+8+20=0

We multiply all the terms by the denominator


3n*2n+8*2n+20*2n-1=0

Wy multiply elements

6n^2+16n+40n-1=0

We add all the numbers together, and all the variables

6n^2+56n-1=0

a = 6; b = 56; c = -1;
Δ = b2-4ac
Δ = 562-4·6·(-1)
Δ = 3160
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:

$\sqrt{\Delta}=\sqrt{3160}=\sqrt{4*790}=\sqrt{4}*\sqrt{790}=2\sqrt{790}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-2\sqrt{790}}{2*6}=\frac{-56-2\sqrt{790}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+2\sqrt{790}}{2*6}=\frac{-56+2\sqrt{790}}{12}
$