-9(5+8d)d=6

Solution for -9(5+8d)d=6 equation:

-9(5+8d)d=6

We move all terms to the left:

-9(5+8d)d-(6)=0

We add all the numbers together, and all the variables

-9(8d+5)d-6=0

We multiply parentheses

-72d^2-45d-6=0

a = -72; b = -45; c = -6;
Δ = b2-4ac
Δ = -452-4·(-72)·(-6)
Δ = 297
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:

$\sqrt{\Delta}=\sqrt{297}=\sqrt{9*33}=\sqrt{9}*\sqrt{33}=3\sqrt{33}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-3\sqrt{33}}{2*-72}=\frac{45-3\sqrt{33}}{-144}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+3\sqrt{33}}{2*-72}=\frac{45+3\sqrt{33}}{-144}
$