u^2-u^-1-36=0

Solution for u^2-u^-1-36=0 equation:

u^2-u^-1-36=0

We add all the numbers together, and all the variables

u^2-1u-37=0

a = 1; b = -1; c = -37;
Δ = b2-4ac
Δ = -12-4·1·(-37)
Δ = 149
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{149}}{2*1}=\frac{1-\sqrt{149}}{2}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{149}}{2*1}=\frac{1+\sqrt{149}}{2}
$