0=n^2-10n+5

Solution for 0=n^2-10n+5 equation:

0=n^2-10n+5

We move all terms to the left:

0-(n^2-10n+5)=0

We add all the numbers together, and all the variables

-(n^2-10n+5)=0

We get rid of parentheses

-n^2+10n-5=0

We add all the numbers together, and all the variables

-1n^2+10n-5=0

a = -1; b = 10; c = -5;
Δ = b2-4ac
Δ = 102-4·(-1)·(-5)
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-4\sqrt{5}}{2*-1}=\frac{-10-4\sqrt{5}}{-2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+4\sqrt{5}}{2*-1}=\frac{-10+4\sqrt{5}}{-2}
$