d(d-8)=8

Solution for d(d-8)=8 equation:

d(d-8)=8

We move all terms to the left:

d(d-8)-(8)=0

We multiply parentheses

d^2-8d-8=0

a = 1; b = -8; c = -8;
Δ = b2-4ac
Δ = -82-4·1·(-8)
Δ = 96
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{6}}{2*1}=\frac{8-4\sqrt{6}}{2}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{6}}{2*1}=\frac{8+4\sqrt{6}}{2}
$