X(x-1)=48

Solution for X(x-1)=48 equation:

X(X-1)=48

We move all terms to the left:

X(X-1)-(48)=0

We multiply parentheses

X^2-1X-48=0

a = 1; b = -1; c = -48;
Δ = b2-4ac
Δ = -12-4·1·(-48)
Δ = 193
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{193}}{2*1}=\frac{1-\sqrt{193}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{193}}{2*1}=\frac{1+\sqrt{193}}{2}
$