2/7x+1/5x=51

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Solution for 2/7x+1/5x=51 equation:



2/7x+1/5x=51
We move all terms to the left:
2/7x+1/5x-(51)=0
Domain of the equation: 7x!=0
x!=0/7
x!=0
x∈R
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
We calculate fractions
10x/35x^2+7x/35x^2-51=0
We multiply all the terms by the denominator
10x+7x-51*35x^2=0
We add all the numbers together, and all the variables
17x-51*35x^2=0
Wy multiply elements
-1785x^2+17x=0
a = -1785; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-1785)·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*-1785}=\frac{-34}{-3570} =1/105 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-1785}=\frac{0}{-3570} =0 $

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