5/x-18=2x-9

Solution for 5/x-18=2x-9 equation:

5/x-18=2x-9

We move all terms to the left:

5/x-18-(2x-9)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

5/x-2x+9-18=0

We multiply all the terms by the denominator


-2x*x+9*x-18*x+5=0

We add all the numbers together, and all the variables

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

Wy multiply elements

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

a = -2; b = -9; c = +5;
Δ = b2-4ac
Δ = -92-4·(-2)·5
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-11}{2*-2}=\frac{-2}{-4}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+11}{2*-2}=\frac{20}{-4}
=-5
$