5+2(n+1)=2n2

Solution for 5+2(n+1)=2n2 equation:

5+2(n+1)=2n^2

We move all terms to the left:

5+2(n+1)-(2n^2)=0

determiningTheFunctionDomain
-2n^2+2(n+1)+5=0

We multiply parentheses

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

We add all the numbers together, and all the variables

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

a = -2; b = 2; c = +7;
Δ = b2-4ac
Δ = 22-4·(-2)·7
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{15}}{2*-2}=\frac{-2-2\sqrt{15}}{-4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{15}}{2*-2}=\frac{-2+2\sqrt{15}}{-4}
$