1/2d-12=24d

Solution for 1/2d-12=24d equation:

1/2d-12=24d

We move all terms to the left:

1/2d-12-(24d)=0


Domain of the equation: 2d!=0

d!=0/2

d!=0

d∈R


We add all the numbers together, and all the variables

-24d+1/2d-12=0

We multiply all the terms by the denominator


-24d*2d-12*2d+1=0

Wy multiply elements

-48d^2-24d+1=0

a = -48; b = -24; c = +1;
Δ = b2-4ac
Δ = -242-4·(-48)·1
Δ = 768
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:

$\sqrt{\Delta}=\sqrt{768}=\sqrt{256*3}=\sqrt{256}*\sqrt{3}=16\sqrt{3}$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-16\sqrt{3}}{2*-48}=\frac{24-16\sqrt{3}}{-96}
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+16\sqrt{3}}{2*-48}=\frac{24+16\sqrt{3}}{-96}
$