x*x-x-32=0

Solution for x*x-x-32=0 equation:

x*x-x-32=0

We add all the numbers together, and all the variables

-1x+x*x-32=0

Wy multiply elements

x^2-1x-32=0

a = 1; b = -1; c = -32;
Δ = b2-4ac
Δ = -12-4·1·(-32)
Δ = 129
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{129}}{2*1}=\frac{1-\sqrt{129}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{129}}{2*1}=\frac{1+\sqrt{129}}{2}
$