12d+9=4d2

Solution for 12d+9=4d2 equation:

12d+9=4d^2

We move all terms to the left:

12d+9-(4d^2)=0

determiningTheFunctionDomain
-4d^2+12d+9=0

a = -4; b = 12; c = +9;
Δ = b2-4ac
Δ = 122-4·(-4)·9
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12\sqrt{2}}{2*-4}=\frac{-12-12\sqrt{2}}{-8}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12\sqrt{2}}{2*-4}=\frac{-12+12\sqrt{2}}{-8}
$