x(x+4)=64

Solution for x(x+4)=64 equation:

x(x+4)=64

We move all terms to the left:

x(x+4)-(64)=0

We multiply parentheses

x^2+4x-64=0

a = 1; b = 4; c = -64;
Δ = b2-4ac
Δ = 42-4·1·(-64)
Δ = 272
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:

$\sqrt{\Delta}=\sqrt{272}=\sqrt{16*17}=\sqrt{16}*\sqrt{17}=4\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{17}}{2*1}=\frac{-4-4\sqrt{17}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{17}}{2*1}=\frac{-4+4\sqrt{17}}{2}
$