(2n+7)2=14n2

Solution for (2n+7)2=14n2 equation:

(2n+7)2=14n^2

We move all terms to the left:

(2n+7)2-(14n^2)=0

determiningTheFunctionDomain
-14n^2+(2n+7)2=0

We multiply parentheses

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

a = -14; b = 4; c = +14;
Δ = b2-4ac
Δ = 42-4·(-14)·14
Δ = 800
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:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-20\sqrt{2}}{2*-14}=\frac{-4-20\sqrt{2}}{-28}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+20\sqrt{2}}{2*-14}=\frac{-4+20\sqrt{2}}{-28}
$