x^2-x-506=0

Solution for x^2-x-506=0 equation:

x^2-x-506=0

We add all the numbers together, and all the variables

x^2-1x-506=0

a = 1; b = -1; c = -506;
Δ = b2-4ac
Δ = -12-4·1·(-506)
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-45}{2*1}=\frac{-44}{2}
=-22
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+45}{2*1}=\frac{46}{2}
=23
$