x-5/x=3x-9

Solution for x-5/x=3x-9 equation:

x-5/x=3x-9

We move all terms to the left:

x-5/x-(3x-9)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

x-5/x-3x+9=0

We multiply all the terms by the denominator


x*x-3x*x+9*x-5=0

We add all the numbers together, and all the variables

9x+x*x-3x*x-5=0

Wy multiply elements

x^2-3x^2+9x-5=0

We add all the numbers together, and all the variables

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

a = -2; b = 9; c = -5;
Δ = b2-4ac
Δ = 92-4·(-2)·(-5)
Δ = 41
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{-(9)-\sqrt{41}}{2*-2}=\frac{-9-\sqrt{41}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{41}}{2*-2}=\frac{-9+\sqrt{41}}{-4}
$