9/x-7=5x

Solution for 9/x-7=5x equation:

9/x-7=5x

We move all terms to the left:

9/x-7-(5x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-5x+9/x-7=0

We multiply all the terms by the denominator


-5x*x-7*x+9=0

We add all the numbers together, and all the variables

-7x-5x*x+9=0

Wy multiply elements

-5x^2-7x+9=0

a = -5; b = -7; c = +9;
Δ = b2-4ac
Δ = -72-4·(-5)·9
Δ = 229
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{229}}{2*-5}=\frac{7-\sqrt{229}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{229}}{2*-5}=\frac{7+\sqrt{229}}{-10}
$