n2-6n+3=3n-16

Solution for n2-6n+3=3n-16 equation:

n2-6n+3=3n-16

We move all terms to the left:

n2-6n+3-(3n-16)=0

We add all the numbers together, and all the variables

n^2-6n-(3n-16)+3=0

We get rid of parentheses

n^2-6n-3n+16+3=0

We add all the numbers together, and all the variables

n^2-9n+19=0

a = 1; b = -9; c = +19;
Δ = b2-4ac
Δ = -92-4·1·19
Δ = 5
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{-(-9)-\sqrt{5}}{2*1}=\frac{9-\sqrt{5}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{5}}{2*1}=\frac{9+\sqrt{5}}{2}
$