x(x+16)=12^2

Solution for x(x+16)=12^2 equation:

x(x+16)=12^2

We move all terms to the left:

x(x+16)-(12^2)=0

We add all the numbers together, and all the variables

x(x+16)-144=0

We multiply parentheses

x^2+16x-144=0

a = 1; b = 16; c = -144;
Δ = b2-4ac
Δ = 162-4·1·(-144)
Δ = 832
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:

$\sqrt{\Delta}=\sqrt{832}=\sqrt{64*13}=\sqrt{64}*\sqrt{13}=8\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-8\sqrt{13}}{2*1}=\frac{-16-8\sqrt{13}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+8\sqrt{13}}{2*1}=\frac{-16+8\sqrt{13}}{2}
$