x(x+12)=320

Solution for x(x+12)=320 equation:

x(x+12)=320

We move all terms to the left:

x(x+12)-(320)=0

We multiply parentheses

x^2+12x-320=0

a = 1; b = 12; c = -320;
Δ = b2-4ac
Δ = 122-4·1·(-320)
Δ = 1424
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:

$\sqrt{\Delta}=\sqrt{1424}=\sqrt{16*89}=\sqrt{16}*\sqrt{89}=4\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{89}}{2*1}=\frac{-12-4\sqrt{89}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{89}}{2*1}=\frac{-12+4\sqrt{89}}{2}
$