D/12d=6d+24

Solution for D/12d=6d+24 equation:

/12D=6D+24

We move all terms to the left:

/12D-(6D+24)=0


Domain of the equation: 12D!=0

D!=0/12

D!=0

D∈R


We get rid of parentheses

/12D-6D-24=0

We multiply all the terms by the denominator


-6D*12D-24*12D+=0

We add all the numbers together, and all the variables

-6D*12D-24*12D=0

Wy multiply elements

-72D^2-288D=0

a = -72; b = -288; c = 0;
Δ = b2-4ac
Δ = -2882-4·(-72)·0
Δ = 82944
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$D_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$D_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{82944}=288$
$D_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-288)-288}{2*-72}=\frac{0}{-144}
=0
$
$D_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-288)+288}{2*-72}=\frac{576}{-144}
=-4
$