x(x+16)=-52

Solution for x(x+16)=-52 equation:

x(x+16)=-52

We move all terms to the left:

x(x+16)-(-52)=0

We add all the numbers together, and all the variables

x(x+16)+52=0

We multiply parentheses

x^2+16x+52=0

a = 1; b = 16; c = +52;
Δ = b2-4ac
Δ = 162-4·1·52
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{3}}{2*1}=\frac{-16-4\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{3}}{2*1}=\frac{-16+4\sqrt{3}}{2}
$