18d+81=d^2

Solution for 18d+81=d^2 equation:

18d+81=d^2

We move all terms to the left:

18d+81-(d^2)=0

determiningTheFunctionDomain
-d^2+18d+81=0

We add all the numbers together, and all the variables

-1d^2+18d+81=0

a = -1; b = 18; c = +81;
Δ = b2-4ac
Δ = 182-4·(-1)·81
Δ = 648
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:

$\sqrt{\Delta}=\sqrt{648}=\sqrt{324*2}=\sqrt{324}*\sqrt{2}=18\sqrt{2}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18\sqrt{2}}{2*-1}=\frac{-18-18\sqrt{2}}{-2}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18\sqrt{2}}{2*-1}=\frac{-18+18\sqrt{2}}{-2}
$