(8+x)(x)=648

Solution for (8+x)(x)=648 equation:

(8+x)(x)=648

We move all terms to the left:

(8+x)(x)-(648)=0

We add all the numbers together, and all the variables

(x+8)x-648=0

We multiply parentheses

x^2+8x-648=0

a = 1; b = 8; c = -648;
Δ = b2-4ac
Δ = 82-4·1·(-648)
Δ = 2656
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:

$\sqrt{\Delta}=\sqrt{2656}=\sqrt{16*166}=\sqrt{16}*\sqrt{166}=4\sqrt{166}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{166}}{2*1}=\frac{-8-4\sqrt{166}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{166}}{2*1}=\frac{-8+4\sqrt{166}}{2}
$