5/2*4n=18+4*n

Solution for 5/2*4n=18+4*n equation:

5/2*4n=18+4n

We move all terms to the left:

5/2*4n-(18+4n)=0


Domain of the equation: 2*4n!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

5/2*4n-(4n+18)=0

We get rid of parentheses

5/2*4n-4n-18=0

We multiply all the terms by the denominator


-4n*2*4n-18*2*4n+5=0

Wy multiply elements

-32n^2*4-144n*4+5=0

Wy multiply elements

-128n^2-576n+5=0

a = -128; b = -576; c = +5;
Δ = b2-4ac
Δ = -5762-4·(-128)·5
Δ = 334336
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:

$\sqrt{\Delta}=\sqrt{334336}=\sqrt{256*1306}=\sqrt{256}*\sqrt{1306}=16\sqrt{1306}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-576)-16\sqrt{1306}}{2*-128}=\frac{576-16\sqrt{1306}}{-256}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-576)+16\sqrt{1306}}{2*-128}=\frac{576+16\sqrt{1306}}{-256}
$