1/4d-2/5d=39

Solution for 1/4d-2/5d=39 equation:

1/4d-2/5d=39

We move all terms to the left:

1/4d-2/5d-(39)=0


Domain of the equation: 4d!=0

d!=0/4

d!=0

d∈R



Domain of the equation: 5d!=0

d!=0/5

d!=0

d∈R


We calculate fractions


5d/20d^2+(-8d)/20d^2-39=0

We multiply all the terms by the denominator


5d+(-8d)-39*20d^2=0

Wy multiply elements

-780d^2+5d+(-8d)=0

We get rid of parentheses

-780d^2+5d-8d=0

We add all the numbers together, and all the variables

-780d^2-3d=0

a = -780; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-780)·0
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{-(-3)-3}{2*-780}=\frac{0}{-1560}
=0
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-780}=\frac{6}{-1560}
=-1/260
$