(X)x(X-1)=63

Solution for (X)x(X-1)=63 equation:

(X)X(X-1)=63

We move all terms to the left:

(X)X(X-1)-(63)=0

We multiply parentheses

X^2-1X-63=0

a = 1; b = -1; c = -63;
Δ = b2-4ac
Δ = -12-4·1·(-63)
Δ = 253
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{253}}{2*1}=\frac{1-\sqrt{253}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{253}}{2*1}=\frac{1+\sqrt{253}}{2}
$