1/x=16/(9x)+7

Solution for 1/x=16/(9x)+7 equation:

1/x=16/(9x)+7

We move all terms to the left:

1/x-(16/(9x)+7)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 9x+7)!=0

x∈R


We get rid of parentheses

1/x-16/9x-7=0

We calculate fractions


9x/9x^2+(-16x)/9x^2-7=0

We multiply all the terms by the denominator


9x+(-16x)-7*9x^2=0

Wy multiply elements

-63x^2+9x+(-16x)=0

We get rid of parentheses

-63x^2+9x-16x=0

We add all the numbers together, and all the variables

-63x^2-7x=0

a = -63; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·(-63)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*-63}=\frac{0}{-126}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*-63}=\frac{14}{-126}
=-1/9
$