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^2-8=0

We multiply all the terms by the denominator


10d+(-9d)-8*6d^2=0

Wy multiply elements

-48d^2+10d+(-9d)=0

We get rid of parentheses

-48d^2+10d-9d=0

We add all the numbers together, and all the variables

-48d^2+d=0

a = -48; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-48)·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*-48}=\frac{-2}{-96}
=1/48
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-48}=\frac{0}{-96}
=0
$