x^2-x+36=90

Solution for x^2-x+36=90 equation:

x^2-x+36=90

We move all terms to the left:

x^2-x+36-(90)=0

We add all the numbers together, and all the variables

x^2-1x-54=0

a = 1; b = -1; c = -54;
Δ = b2-4ac
Δ = -12-4·1·(-54)
Δ = 217
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{217}}{2*1}=\frac{1-\sqrt{217}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{217}}{2*1}=\frac{1+\sqrt{217}}{2}
$