2n+24=2/7n

Solution for 2n+24=2/7n equation:

2n+24=2/7n

We move all terms to the left:

2n+24-(2/7n)=0


Domain of the equation: 7n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

2n-(+2/7n)+24=0

We get rid of parentheses

2n-2/7n+24=0

We multiply all the terms by the denominator


2n*7n+24*7n-2=0

Wy multiply elements

14n^2+168n-2=0

a = 14; b = 168; c = -2;
Δ = b2-4ac
Δ = 1682-4·14·(-2)
Δ = 28336
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:

$\sqrt{\Delta}=\sqrt{28336}=\sqrt{16*1771}=\sqrt{16}*\sqrt{1771}=4\sqrt{1771}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(168)-4\sqrt{1771}}{2*14}=\frac{-168-4\sqrt{1771}}{28}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(168)+4\sqrt{1771}}{2*14}=\frac{-168+4\sqrt{1771}}{28}
$