2x+1/7x=18

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Solution for 2x+1/7x=18 equation: 



2x+1/7x=18

We move all terms to the left:

2x+1/7x-(18)=0



Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



We multiply all the terms by the denominator


2x*7x-18*7x+1=0

Wy multiply elements

14x^2-126x+1=0

a = 14; b = -126; c = +1;
Δ = b2-4ac
Δ = -1262-4·14·1
Δ = 15820
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:


$\sqrt{\Delta}=\sqrt{15820}=\sqrt{4*3955}=\sqrt{4}*\sqrt{3955}=2\sqrt{3955}$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-126)-2\sqrt{3955}}{2*14}=\frac{126-2\sqrt{3955}}{28}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-126)+2\sqrt{3955}}{2*14}=\frac{126+2\sqrt{3955}}{28}
$

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