1/4x+84/20=-4/3x

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Solution for 1/4x+84/20=-4/3x equation: 



1/4x+84/20=-4/3x

We move all terms to the left:

1/4x+84/20-(-4/3x)=0



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R





Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R



We get rid of parentheses

1/4x+4/3x+84/20=0

We calculate fractions


3024x^2/480x^2+120x/480x^2+640x/480x^2=0

We multiply all the terms by the denominator


3024x^2+120x+640x=0

We add all the numbers together, and all the variables

3024x^2+760x=0

a = 3024; b = 760; c = 0;
Δ = b2-4ac
Δ = 7602-4·3024·0
Δ = 577600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{577600}=760$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(760)-760}{2*3024}=\frac{-1520}{6048}
=-95/378
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(760)+760}{2*3024}=\frac{0}{6048}
=0
$

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