2/7x+5/49x=-19

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Solution for 2/7x+5/49x=-19 equation:



2/7x+5/49x=-19
We move all terms to the left:
2/7x+5/49x-(-19)=0
Domain of the equation: 7x!=0
x!=0/7
x!=0
x∈R
Domain of the equation: 49x!=0
x!=0/49
x!=0
x∈R
We add all the numbers together, and all the variables
2/7x+5/49x+19=0
We calculate fractions
98x/343x^2+35x/343x^2+19=0
We multiply all the terms by the denominator
98x+35x+19*343x^2=0
We add all the numbers together, and all the variables
133x+19*343x^2=0
Wy multiply elements
6517x^2+133x=0
a = 6517; b = 133; c = 0;
Δ = b2-4ac
Δ = 1332-4·6517·0
Δ = 17689
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{17689}=133$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(133)-133}{2*6517}=\frac{-266}{13034} =-1/49 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(133)+133}{2*6517}=\frac{0}{13034} =0 $

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