x(x+24)=56

Solution for x(x+24)=56 equation:

x(x+24)=56

We move all terms to the left:

x(x+24)-(56)=0

We multiply parentheses

x^2+24x-56=0

a = 1; b = 24; c = -56;
Δ = b2-4ac
Δ = 242-4·1·(-56)
Δ = 800
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:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-20\sqrt{2}}{2*1}=\frac{-24-20\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+20\sqrt{2}}{2*1}=\frac{-24+20\sqrt{2}}{2}
$