X(x-1)=231

Solution for X(x-1)=231 equation:

X(X-1)=231

We move all terms to the left:

X(X-1)-(231)=0

We multiply parentheses

X^2-1X-231=0

a = 1; b = -1; c = -231;
Δ = b2-4ac
Δ = -12-4·1·(-231)
Δ = 925
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:

$\sqrt{\Delta}=\sqrt{925}=\sqrt{25*37}=\sqrt{25}*\sqrt{37}=5\sqrt{37}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-5\sqrt{37}}{2*1}=\frac{1-5\sqrt{37}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+5\sqrt{37}}{2*1}=\frac{1+5\sqrt{37}}{2}
$