-27=-12d-2d2+5

Solution for -27=-12d-2d2+5 equation:

-27=-12d-2d^2+5

We move all terms to the left:

-27-(-12d-2d^2+5)=0

We get rid of parentheses

2d^2+12d-5-27=0

We add all the numbers together, and all the variables

2d^2+12d-32=0

a = 2; b = 12; c = -32;
Δ = b2-4ac
Δ = 122-4·2·(-32)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-20}{2*2}=\frac{-32}{4}
=-8
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+20}{2*2}=\frac{8}{4}
=2
$