x^2-2x=2.718281828^5

Solution for x^2-2x=2.718281828^5 equation:

x^2-2x=2.718281828^5

We move all terms to the left:

x^2-2x-(2.718281828^5)=0

We add all the numbers together, and all the variables

x^2-2x-148.41315897726=0

a = 1; b = -2; c = -148.41315897726;
Δ = b2-4ac
Δ = -22-4·1·(-148.41315897726)
Δ = 597.65263590904
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{-(-2)-\sqrt{597.65263590904}}{2*1}=\frac{2-\sqrt{597.65263590904}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+\sqrt{597.65263590904}}{2*1}=\frac{2+\sqrt{597.65263590904}}{2}
$