x(x+24)=456

Solution for x(x+24)=456 equation:

x(x+24)=456

We move all terms to the left:

x(x+24)-(456)=0

We multiply parentheses

x^2+24x-456=0

a = 1; b = 24; c = -456;
Δ = b2-4ac
Δ = 242-4·1·(-456)
Δ = 2400
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:

$\sqrt{\Delta}=\sqrt{2400}=\sqrt{400*6}=\sqrt{400}*\sqrt{6}=20\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-20\sqrt{6}}{2*1}=\frac{-24-20\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+20\sqrt{6}}{2*1}=\frac{-24+20\sqrt{6}}{2}
$