1/9x+7x=9

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Solution for 1/9x+7x=9 equation: 



1/9x+7x=9

We move all terms to the left:

1/9x+7x-(9)=0



Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



We add all the numbers together, and all the variables

7x+1/9x-9=0

We multiply all the terms by the denominator


7x*9x-9*9x+1=0

Wy multiply elements

63x^2-81x+1=0

a = 63; b = -81; c = +1;
Δ = b2-4ac
Δ = -812-4·63·1
Δ = 6309
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:


$\sqrt{\Delta}=\sqrt{6309}=\sqrt{9*701}=\sqrt{9}*\sqrt{701}=3\sqrt{701}$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-81)-3\sqrt{701}}{2*63}=\frac{81-3\sqrt{701}}{126}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-81)+3\sqrt{701}}{2*63}=\frac{81+3\sqrt{701}}{126}
$

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