1/3d-22/3-71/2d-71/2=7/12

Solution for 1/3d-22/3-71/2d-71/2=7/12 equation:

1/3d-22/3-71/2d-71/2=7/12

We move all terms to the left:

1/3d-22/3-71/2d-71/2-(7/12)=0


Domain of the equation: 3d!=0

d!=0/3

d!=0

d∈R



Domain of the equation: 2d!=0

d!=0/2

d!=0

d∈R


We add all the numbers together, and all the variables

1/3d-71/2d-22/3-71/2-(+7/12)=0

We get rid of parentheses

1/3d-71/2d-22/3-71/2-7/12=0

We calculate fractions


(-504d^2)/1296d^2+96d/1296d^2+(-23004d)/1296d^2+(-2112d)/1296d^2+(-23004d)/1296d^2=0

We multiply all the terms by the denominator


(-504d^2)+96d+(-23004d)+(-2112d)+(-23004d)=0

We get rid of parentheses

-504d^2+96d-23004d-2112d-23004d=0

We add all the numbers together, and all the variables

-504d^2-48024d=0

a = -504; b = -48024; c = 0;
Δ = b2-4ac
Δ = -480242-4·(-504)·0
Δ = 2306304576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2306304576}=48024$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48024)-48024}{2*-504}=\frac{0}{-1008}
=0
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48024)+48024}{2*-504}=\frac{96048}{-1008}
=-95+2/7
$