X^2-x=101

Solution for X^2-x=101 equation:

X^2-X=101

We move all terms to the left:

X^2-X-(101)=0

We add all the numbers together, and all the variables

X^2-1X-101=0

a = 1; b = -1; c = -101;
Δ = b2-4ac
Δ = -12-4·1·(-101)
Δ = 405
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{405}=\sqrt{81*5}=\sqrt{81}*\sqrt{5}=9\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-9\sqrt{5}}{2*1}=\frac{1-9\sqrt{5}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+9\sqrt{5}}{2*1}=\frac{1+9\sqrt{5}}{2}
$