n^2-10n+50=8n-16

Solution for n^2-10n+50=8n-16 equation:

n^2-10n+50=8n-16

We move all terms to the left:

n^2-10n+50-(8n-16)=0

We get rid of parentheses

n^2-10n-8n+16+50=0

We add all the numbers together, and all the variables

n^2-18n+66=0

a = 1; b = -18; c = +66;
Δ = b2-4ac
Δ = -182-4·1·66
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{15}}{2*1}=\frac{18-2\sqrt{15}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{15}}{2*1}=\frac{18+2\sqrt{15}}{2}
$