12d^2-5d-8=-5

Solution for 12d^2-5d-8=-5 equation:

12d^2-5d-8=-5

We move all terms to the left:

12d^2-5d-8-(-5)=0

We add all the numbers together, and all the variables

12d^2-5d-3=0

a = 12; b = -5; c = -3;
Δ = b2-4ac
Δ = -52-4·12·(-3)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-13}{2*12}=\frac{-8}{24}
=-1/3
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+13}{2*12}=\frac{18}{24}
=3/4
$