x^2+x-10^18=0

Solution for x^2+x-10^18=0 equation:

x^2+x-10^18=0

We add all the numbers together, and all the variables

x^2+x-1000000000000000000=0

a = 1; b = 1; c = -1000000000000000000;
Δ = b2-4ac
Δ = 12-4·1·(-1000000000000000000)
Δ = 4000000000000000001
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4000000000000000001}=2000000000$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-2000000000}{2*1}=\frac{-2000000001}{2}
=-1000000000+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+2000000000}{2*1}=\frac{1999999999}{2}
=999999999+1/2
$