X^2-x-127=0

Solution for X^2-x-127=0 equation:

X^2-X-127=0

We add all the numbers together, and all the variables

X^2-1X-127=0

a = 1; b = -1; c = -127;
Δ = b2-4ac
Δ = -12-4·1·(-127)
Δ = 509
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{509}}{2*1}=\frac{1-\sqrt{509}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{509}}{2*1}=\frac{1+\sqrt{509}}{2}
$