593=X^2+x+41

Solution for 593=X^2+x+41 equation:

593=X^2+X+41

We move all terms to the left:

593-(X^2+X+41)=0

We get rid of parentheses

-X^2-X-41+593=0

We add all the numbers together, and all the variables

-1X^2-1X+552=0

a = -1; b = -1; c = +552;
Δ = b2-4ac
Δ = -12-4·(-1)·552
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-47}{2*-1}=\frac{-46}{-2}
=+23
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+47}{2*-1}=\frac{48}{-2}
=-24
$