n^2-8n=3n-12

Solution for n^2-8n=3n-12 equation:

n^2-8n=3n-12

We move all terms to the left:

n^2-8n-(3n-12)=0

We get rid of parentheses

n^2-8n-3n+12=0

We add all the numbers together, and all the variables

n^2-11n+12=0

a = 1; b = -11; c = +12;
Δ = b2-4ac
Δ = -112-4·1·12
Δ = 73
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{73}}{2*1}=\frac{11-\sqrt{73}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{73}}{2*1}=\frac{11+\sqrt{73}}{2}
$