7/x-3=9x.

Solution for 7/x-3=9x. equation:

7/x-3=9x.

We move all terms to the left:

7/x-3-(9x.)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

7/x-(+9x.)-3=0

We get rid of parentheses

7/x-9x.-3=0

We multiply all the terms by the denominator


-(9x.)*x-3*x+7=0

We add all the numbers together, and all the variables

-(+9x.)*x-3*x+7=0

We add all the numbers together, and all the variables

-3x-(+9x.)*x+7=0

We multiply parentheses

-9x^2-3x+7=0

a = -9; b = -3; c = +7;
Δ = b2-4ac
Δ = -32-4·(-9)·7
Δ = 261
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:

$\sqrt{\Delta}=\sqrt{261}=\sqrt{9*29}=\sqrt{9}*\sqrt{29}=3\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{29}}{2*-9}=\frac{3-3\sqrt{29}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{29}}{2*-9}=\frac{3+3\sqrt{29}}{-18}
$