9/x-3=2x+1

Solution for 9/x-3=2x+1 equation:

9/x-3=2x+1

We move all terms to the left:

9/x-3-(2x+1)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

9/x-2x-1-3=0

We multiply all the terms by the denominator


-2x*x-1*x-3*x+9=0

We add all the numbers together, and all the variables

-4x-2x*x+9=0

Wy multiply elements

-2x^2-4x+9=0

a = -2; b = -4; c = +9;
Δ = b2-4ac
Δ = -42-4·(-2)·9
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{22}}{2*-2}=\frac{4-2\sqrt{22}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{22}}{2*-2}=\frac{4+2\sqrt{22}}{-4}
$