x(x-1)=245

Solution for x(x-1)=245 equation:

x(x-1)=245

We move all terms to the left:

x(x-1)-(245)=0

We multiply parentheses

x^2-1x-245=0

a = 1; b = -1; c = -245;
Δ = b2-4ac
Δ = -12-4·1·(-245)
Δ = 981
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:

$\sqrt{\Delta}=\sqrt{981}=\sqrt{9*109}=\sqrt{9}*\sqrt{109}=3\sqrt{109}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-3\sqrt{109}}{2*1}=\frac{1-3\sqrt{109}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+3\sqrt{109}}{2*1}=\frac{1+3\sqrt{109}}{2}
$