5n=5(2n)^2

Solution for 5n=5(2n)^2 equation:

5n=5(2n)^2

We move all terms to the left:

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

determiningTheFunctionDomain
5n-52n^2=0

We add all the numbers together, and all the variables

-52n^2+5n=0

a = -52; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-52)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-52}=\frac{-10}{-104}
=5/52
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-52}=\frac{0}{-104}
=0
$