(9+2)(d+6)-d(d+3)=37

Solution for (9+2)(d+6)-d(d+3)=37 equation:

(9+2)(d+6)-d(d+3)=37

We move all terms to the left:

(9+2)(d+6)-d(d+3)-(37)=0

We add all the numbers together, and all the variables

11(d+6)-d(d+3)-37=0

We multiply parentheses

-d^2+11d-3d+66-37=0

We add all the numbers together, and all the variables

-1d^2+8d+29=0

a = -1; b = 8; c = +29;
Δ = b2-4ac
Δ = 82-4·(-1)·29
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-6\sqrt{5}}{2*-1}=\frac{-8-6\sqrt{5}}{-2}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+6\sqrt{5}}{2*-1}=\frac{-8+6\sqrt{5}}{-2}
$