x^2-x-1=89

Solution for x^2-x-1=89 equation:

x^2-x-1=89

We move all terms to the left:

x^2-x-1-(89)=0

We add all the numbers together, and all the variables

x^2-1x-90=0

a = 1; b = -1; c = -90;
Δ = b2-4ac
Δ = -12-4·1·(-90)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-19}{2*1}=\frac{-18}{2}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+19}{2*1}=\frac{20}{2}
=10
$