x(x-1)=182

Solution for x(x-1)=182 equation:

x(x-1)=182

We move all terms to the left:

x(x-1)-(182)=0

We multiply parentheses

x^2-1x-182=0

a = 1; b = -1; c = -182;
Δ = b2-4ac
Δ = -12-4·1·(-182)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-27}{2*1}=\frac{-26}{2}
=-13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+27}{2*1}=\frac{28}{2}
=14
$