x(x+8)=486

Solution for x(x+8)=486 equation:

x(x+8)=486

We move all terms to the left:

x(x+8)-(486)=0

We multiply parentheses

x^2+8x-486=0

a = 1; b = 8; c = -486;
Δ = b2-4ac
Δ = 82-4·1·(-486)
Δ = 2008
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:

$\sqrt{\Delta}=\sqrt{2008}=\sqrt{4*502}=\sqrt{4}*\sqrt{502}=2\sqrt{502}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{502}}{2*1}=\frac{-8-2\sqrt{502}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{502}}{2*1}=\frac{-8+2\sqrt{502}}{2}
$