2+7n=2-9+5n(2)

Solution for 2+7n=2-9+5n(2) equation:

2+7n=2-9+5n(2)

We move all terms to the left:

2+7n-(2-9+5n(2))=0

We add all the numbers together, and all the variables

-(+5n^2+2-9)+7n+2=0

We get rid of parentheses

-5n^2+7n-2+9+2=0

We add all the numbers together, and all the variables

-5n^2+7n+9=0

a = -5; b = 7; c = +9;
Δ = b2-4ac
Δ = 72-4·(-5)·9
Δ = 229
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{-(7)-\sqrt{229}}{2*-5}=\frac{-7-\sqrt{229}}{-10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{229}}{2*-5}=\frac{-7+\sqrt{229}}{-10}
$