8/x+7-7/3x+21=0

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Solution for 8/x+7-7/3x+21=0 equation: 



8/x+7-7/3x+21=0



Domain of the equation: x!=0

x∈R





Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



We add all the numbers together, and all the variables

8/x-7/3x+28=0

We calculate fractions


24x/3x^2+(-7x)/3x^2+28=0

We multiply all the terms by the denominator


24x+(-7x)+28*3x^2=0

Wy multiply elements

84x^2+24x+(-7x)=0

We get rid of parentheses

84x^2+24x-7x=0

We add all the numbers together, and all the variables

84x^2+17x=0

a = 84; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·84·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*84}=\frac{-34}{168}
=-17/84
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*84}=\frac{0}{168}
=0
$

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