n^2-5n+2=19

Solution for n^2-5n+2=19 equation:

n^2-5n+2=19

We move all terms to the left:

n^2-5n+2-(19)=0

We add all the numbers together, and all the variables

n^2-5n-17=0

a = 1; b = -5; c = -17;
Δ = b2-4ac
Δ = -52-4·1·(-17)
Δ = 93
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{-(-5)-\sqrt{93}}{2*1}=\frac{5-\sqrt{93}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{93}}{2*1}=\frac{5+\sqrt{93}}{2}
$