-16d(d+1)=-29

Solution for -16d(d+1)=-29 equation:

-16d(d+1)=-29

We move all terms to the left:

-16d(d+1)-(-29)=0

We add all the numbers together, and all the variables

-16d(d+1)+29=0

We multiply parentheses

-16d^2-16d+29=0

a = -16; b = -16; c = +29;
Δ = b2-4ac
Δ = -162-4·(-16)·29
Δ = 2112
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:

$\sqrt{\Delta}=\sqrt{2112}=\sqrt{64*33}=\sqrt{64}*\sqrt{33}=8\sqrt{33}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-8\sqrt{33}}{2*-16}=\frac{16-8\sqrt{33}}{-32}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8\sqrt{33}}{2*-16}=\frac{16+8\sqrt{33}}{-32}
$