9/x-15x=58

Solution for 9/x-15x=58 equation:

9/x-15x=58

We move all terms to the left:

9/x-15x-(58)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-15x+9/x-58=0

We multiply all the terms by the denominator


-15x*x-58*x+9=0

We add all the numbers together, and all the variables

-58x-15x*x+9=0

Wy multiply elements

-15x^2-58x+9=0

a = -15; b = -58; c = +9;
Δ = b2-4ac
Δ = -582-4·(-15)·9
Δ = 3904
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:

$\sqrt{\Delta}=\sqrt{3904}=\sqrt{64*61}=\sqrt{64}*\sqrt{61}=8\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-58)-8\sqrt{61}}{2*-15}=\frac{58-8\sqrt{61}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-58)+8\sqrt{61}}{2*-15}=\frac{58+8\sqrt{61}}{-30}
$