7d-4d(d+8)=-8

Solution for 7d-4d(d+8)=-8 equation:

7d-4d(d+8)=-8

We move all terms to the left:

7d-4d(d+8)-(-8)=0

We add all the numbers together, and all the variables

7d-4d(d+8)+8=0

We multiply parentheses

-4d^2+7d-32d+8=0

We add all the numbers together, and all the variables

-4d^2-25d+8=0

a = -4; b = -25; c = +8;
Δ = b2-4ac
Δ = -252-4·(-4)·8
Δ = 753
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-\sqrt{753}}{2*-4}=\frac{25-\sqrt{753}}{-8}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+\sqrt{753}}{2*-4}=\frac{25+\sqrt{753}}{-8}
$