47=n^2-5n+2

Solution for 47=n^2-5n+2 equation:

47=n^2-5n+2

We move all terms to the left:

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

We get rid of parentheses

-n^2+5n-2+47=0

We add all the numbers together, and all the variables

-1n^2+5n+45=0

a = -1; b = 5; c = +45;
Δ = b2-4ac
Δ = 52-4·(-1)·45
Δ = 205
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{205}}{2*-1}=\frac{-5-\sqrt{205}}{-2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{205}}{2*-1}=\frac{-5+\sqrt{205}}{-2}
$