X^2-x=106

Solution for X^2-x=106 equation:

X^2-X=106

We move all terms to the left:

X^2-X-(106)=0

We add all the numbers together, and all the variables

X^2-1X-106=0

a = 1; b = -1; c = -106;
Δ = b2-4ac
Δ = -12-4·1·(-106)
Δ = 425
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:

$\sqrt{\Delta}=\sqrt{425}=\sqrt{25*17}=\sqrt{25}*\sqrt{17}=5\sqrt{17}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-5\sqrt{17}}{2*1}=\frac{1-5\sqrt{17}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+5\sqrt{17}}{2*1}=\frac{1+5\sqrt{17}}{2}
$