n^2=4(4n+9)

Solution for n^2=4(4n+9) equation:

n^2=4(4n+9)

We move all terms to the left:

n^2-(4(4n+9))=0


We calculate terms in parentheses: -(4(4n+9)), so:

4(4n+9)

We multiply parentheses

16n+36

Back to the equation:

-(16n+36)


We get rid of parentheses

n^2-16n-36=0

a = 1; b = -16; c = -36;
Δ = b2-4ac
Δ = -162-4·1·(-36)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-20}{2*1}=\frac{-4}{2}
=-2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+20}{2*1}=\frac{36}{2}
=18
$