552=x^2+x+41

Solution for 552=x^2+x+41 equation:

552=x^2+x+41

We move all terms to the left:

552-(x^2+x+41)=0

We get rid of parentheses

-x^2-x-41+552=0

We add all the numbers together, and all the variables

-1x^2-1x+511=0

a = -1; b = -1; c = +511;
Δ = b2-4ac
Δ = -12-4·(-1)·511
Δ = 2045
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{2045}}{2*-1}=\frac{1-\sqrt{2045}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{2045}}{2*-1}=\frac{1+\sqrt{2045}}{-2}
$