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

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

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

We move all terms to the left:

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


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(-1/4x)-(+2/5x)-39=0

We get rid of parentheses

-1/4x-2/5x-39=0

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

-780x^2-5x-8x=0

We add all the numbers together, and all the variables

-780x^2-13x=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:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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