x(x+8)=768

Solution for x(x+8)=768 equation:

x(x+8)=768

We move all terms to the left:

x(x+8)-(768)=0

We multiply parentheses

x^2+8x-768=0

a = 1; b = 8; c = -768;
Δ = b2-4ac
Δ = 82-4·1·(-768)
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-56}{2*1}=\frac{-64}{2}
=-32
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+56}{2*1}=\frac{48}{2}
=24
$