6d(4d-5)=4d+12

Solution for 6d(4d-5)=4d+12 equation:

6d(4d-5)=4d+12

We move all terms to the left:

6d(4d-5)-(4d+12)=0

We multiply parentheses

24d^2-30d-(4d+12)=0

We get rid of parentheses

24d^2-30d-4d-12=0

We add all the numbers together, and all the variables

24d^2-34d-12=0

a = 24; b = -34; c = -12;
Δ = b2-4ac
Δ = -342-4·24·(-12)
Δ = 2308
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:

$\sqrt{\Delta}=\sqrt{2308}=\sqrt{4*577}=\sqrt{4}*\sqrt{577}=2\sqrt{577}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{577}}{2*24}=\frac{34-2\sqrt{577}}{48}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{577}}{2*24}=\frac{34+2\sqrt{577}}{48}
$