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

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

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

We move all terms to the left:

-(1)/(4)d-(2)/(5)d-(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^2-13d=0

a = -780; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·(-780)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-13}{2*-780}=\frac{0}{-1560}
=0
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*-780}=\frac{26}{-1560}
=-1/60
$