5/3d-1=3/2d-7

Solution for 5/3d-1=3/2d-7 equation:

5/3d-1=3/2d-7

We move all terms to the left:

5/3d-1-(3/2d-7)=0


Domain of the equation: 3d!=0

d!=0/3

d!=0

d∈R



Domain of the equation: 2d-7)!=0

d∈R


We get rid of parentheses

5/3d-3/2d+7-1=0

We calculate fractions


10d/6d^2+(-9d)/6d^2+7-1=0

We add all the numbers together, and all the variables

10d/6d^2+(-9d)/6d^2+6=0

We multiply all the terms by the denominator


10d+(-9d)+6*6d^2=0

Wy multiply elements

36d^2+10d+(-9d)=0

We get rid of parentheses

36d^2+10d-9d=0

We add all the numbers together, and all the variables

36d^2+d=0

a = 36; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·36·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*36}=\frac{-2}{72}
=-1/36
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*36}=\frac{0}{72}
=0
$