2n+5=-12+4/7n

Solution for 2n+5=-12+4/7n equation:

2n+5=-12+4/7n

We move all terms to the left:

2n+5-(-12+4/7n)=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-(4/7n-12)+5=0

We get rid of parentheses

2n-4/7n+12+5=0

We multiply all the terms by the denominator


2n*7n+12*7n+5*7n-4=0

Wy multiply elements

14n^2+84n+35n-4=0

We add all the numbers together, and all the variables

14n^2+119n-4=0

a = 14; b = 119; c = -4;
Δ = b2-4ac
Δ = 1192-4·14·(-4)
Δ = 14385
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(119)-\sqrt{14385}}{2*14}=\frac{-119-\sqrt{14385}}{28}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(119)+\sqrt{14385}}{2*14}=\frac{-119+\sqrt{14385}}{28}
$