2x-18/x+3=0

Solution for 2x-18/x+3=0 equation:

2x-18/x+3=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


2x*x+3*x-18=0

We add all the numbers together, and all the variables

3x+2x*x-18=0

Wy multiply elements

2x^2+3x-18=0

a = 2; b = 3; c = -18;
Δ = b2-4ac
Δ = 32-4·2·(-18)
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{17}}{2*2}=\frac{-3-3\sqrt{17}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{17}}{2*2}=\frac{-3+3\sqrt{17}}{4}
$