2/7x+x=54

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Solution for 2/7x+x=54 equation: 



2/7x+x=54

We move all terms to the left:

2/7x+x-(54)=0



Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



We add all the numbers together, and all the variables

x+2/7x-54=0

We multiply all the terms by the denominator


x*7x-54*7x+2=0

Wy multiply elements

7x^2-378x+2=0

a = 7; b = -378; c = +2;
Δ = b2-4ac
Δ = -3782-4·7·2
Δ = 142828
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:


$\sqrt{\Delta}=\sqrt{142828}=\sqrt{4*35707}=\sqrt{4}*\sqrt{35707}=2\sqrt{35707}$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-378)-2\sqrt{35707}}{2*7}=\frac{378-2\sqrt{35707}}{14}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-378)+2\sqrt{35707}}{2*7}=\frac{378+2\sqrt{35707}}{14}
$

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