x(x-6)=216

Solution for x(x-6)=216 equation:

x(x-6)=216

We move all terms to the left:

x(x-6)-(216)=0

We multiply parentheses

x^2-6x-216=0

a = 1; b = -6; c = -216;
Δ = b2-4ac
Δ = -62-4·1·(-216)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-30}{2*1}=\frac{-24}{2}
=-12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+30}{2*1}=\frac{36}{2}
=18
$