5/x=-6/(2x)-9

Solution for 5/x=-6/(2x)-9 equation:

5/x=-6/(2x)-9

We move all terms to the left:

5/x-(-6/(2x)-9)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x-9)!=0

x∈R


We get rid of parentheses

5/x+6/2x+9=0

We calculate fractions


10x/2x^2+6x/2x^2+9=0

We multiply all the terms by the denominator


10x+6x+9*2x^2=0

We add all the numbers together, and all the variables

16x+9*2x^2=0

Wy multiply elements

18x^2+16x=0

a = 18; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·18·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*18}=\frac{-32}{36}
=-8/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*18}=\frac{0}{36}
=0
$