x^2-x-1=385

Solution for x^2-x-1=385 equation:

x^2-x-1=385

We move all terms to the left:

x^2-x-1-(385)=0

We add all the numbers together, and all the variables

x^2-1x-386=0

a = 1; b = -1; c = -386;
Δ = b2-4ac
Δ = -12-4·1·(-386)
Δ = 1545
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{1545}}{2*1}=\frac{1-\sqrt{1545}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{1545}}{2*1}=\frac{1+\sqrt{1545}}{2}
$