x^2-20x+93=x

Solution for x^2-20x+93=x equation:

x^2-20x+93=x

We move all terms to the left:

x^2-20x+93-(x)=0

We add all the numbers together, and all the variables

x^2-21x+93=0

a = 1; b = -21; c = +93;
Δ = b2-4ac
Δ = -212-4·1·93
Δ = 69
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{-(-21)-\sqrt{69}}{2*1}=\frac{21-\sqrt{69}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{69}}{2*1}=\frac{21+\sqrt{69}}{2}
$