-9d(6+d)=45

Solution for -9d(6+d)=45 equation:

-9d(6+d)=45

We move all terms to the left:

-9d(6+d)-(45)=0

We add all the numbers together, and all the variables

-9d(d+6)-45=0

We multiply parentheses

-9d^2-54d-45=0

a = -9; b = -54; c = -45;
Δ = b2-4ac
Δ = -542-4·(-9)·(-45)
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-36}{2*-9}=\frac{18}{-18}
=-1
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+36}{2*-9}=\frac{90}{-18}
=-5
$