3(4d+1)-9d=6d(2-d)

Solution for 3(4d+1)-9d=6d(2-d) equation:

3(4d+1)-9d=6d(2-d)

We move all terms to the left:

3(4d+1)-9d-(6d(2-d))=0

We add all the numbers together, and all the variables

3(4d+1)-9d-(6d(-1d+2))=0

We add all the numbers together, and all the variables

-9d+3(4d+1)-(6d(-1d+2))=0

We multiply parentheses

-9d+12d-(6d(-1d+2))+3=0


We calculate terms in parentheses: -(6d(-1d+2)), so:

6d(-1d+2)

We multiply parentheses

-6d^2+12d

Back to the equation:

-(-6d^2+12d)


We add all the numbers together, and all the variables

-(-6d^2+12d)+3d+3=0

We get rid of parentheses

6d^2-12d+3d+3=0

We add all the numbers together, and all the variables

6d^2-9d+3=0

a = 6; b = -9; c = +3;
Δ = b2-4ac
Δ = -92-4·6·3
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3}{2*6}=\frac{6}{12}
=1/2
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3}{2*6}=\frac{12}{12}
=1
$