2+(10+5/2n)+3n=4

Solution for 2+(10+5/2n)+3n=4 equation:

2+(10+5/2n)+3n=4

We move all terms to the left:

2+(10+5/2n)+3n-(4)=0


Domain of the equation: 2n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

(5/2n+10)+3n+2-4=0

We add all the numbers together, and all the variables

3n+(5/2n+10)-2=0

We get rid of parentheses

3n+5/2n+10-2=0

We multiply all the terms by the denominator


3n*2n+10*2n-2*2n+5=0

Wy multiply elements

6n^2+20n-4n+5=0

We add all the numbers together, and all the variables

6n^2+16n+5=0

a = 6; b = 16; c = +5;
Δ = b2-4ac
Δ = 162-4·6·5
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{34}}{2*6}=\frac{-16-2\sqrt{34}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{34}}{2*6}=\frac{-16+2\sqrt{34}}{12}
$