5n^2=5n

Solution for 5n^2=5n equation:

5n^2=5n

We move all terms to the left:

5n^2-(5n)=0

a = 5; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·5·0
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*5}=\frac{0}{10}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*5}=\frac{10}{10}
=1
$