X(x-4)=36

Solution for X(x-4)=36 equation:

X(X-4)=36

We move all terms to the left:

X(X-4)-(36)=0

We multiply parentheses

X^2-4X-36=0

a = 1; b = -4; c = -36;
Δ = b2-4ac
Δ = -42-4·1·(-36)
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{10}}{2*1}=\frac{4-4\sqrt{10}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{10}}{2*1}=\frac{4+4\sqrt{10}}{2}
$