8d+12=d2

Solution for 8d+12=d2 equation:

8d+12=d2

We move all terms to the left:

8d+12-(d2)=0

We add all the numbers together, and all the variables

-1d^2+8d+12=0

a = -1; b = 8; c = +12;
Δ = b2-4ac
Δ = 82-4·(-1)·12
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{7}}{2*-1}=\frac{-8-4\sqrt{7}}{-2}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{7}}{2*-1}=\frac{-8+4\sqrt{7}}{-2}
$