x(x-12)=40

Solution for x(x-12)=40 equation:

x(x-12)=40

We move all terms to the left:

x(x-12)-(40)=0

We multiply parentheses

x^2-12x-40=0

a = 1; b = -12; c = -40;
Δ = b2-4ac
Δ = -122-4·1·(-40)
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{19}}{2*1}=\frac{12-4\sqrt{19}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{19}}{2*1}=\frac{12+4\sqrt{19}}{2}
$