x(x-4)=84

Solution for x(x-4)=84 equation:

x(x-4)=84

We move all terms to the left:

x(x-4)-(84)=0

We multiply parentheses

x^2-4x-84=0

a = 1; b = -4; c = -84;
Δ = b2-4ac
Δ = -42-4·1·(-84)
Δ = 352
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:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{22}}{2*1}=\frac{4-4\sqrt{22}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{22}}{2*1}=\frac{4+4\sqrt{22}}{2}
$