x(x+28)=456

Solution for x(x+28)=456 equation:

x(x+28)=456

We move all terms to the left:

x(x+28)-(456)=0

We multiply parentheses

x^2+28x-456=0

a = 1; b = 28; c = -456;
Δ = b2-4ac
Δ = 282-4·1·(-456)
Δ = 2608
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:

$\sqrt{\Delta}=\sqrt{2608}=\sqrt{16*163}=\sqrt{16}*\sqrt{163}=4\sqrt{163}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-4\sqrt{163}}{2*1}=\frac{-28-4\sqrt{163}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+4\sqrt{163}}{2*1}=\frac{-28+4\sqrt{163}}{2}
$