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

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

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

We move all terms to the left:

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


Domain of the equation: 3d!=0

d!=0/3

d!=0

d∈R



Domain of the equation: 5d!=0

d!=0/5

d!=0

d∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-75d^2)/60d^2+20d/60d^2+(-12d)/60d^2=0

We multiply all the terms by the denominator


(-75d^2)+20d+(-12d)=0

We get rid of parentheses

-75d^2+20d-12d=0

We add all the numbers together, and all the variables

-75d^2+8d=0

a = -75; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-75)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-75}=\frac{-16}{-150}
=8/75
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-75}=\frac{0}{-150}
=0
$