9-4x=18/5x

Solution for 9-4x=18/5x equation:

9-4x=18/5x

We move all terms to the left:

9-4x-(18/5x)=0


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-4x-(+18/5x)+9=0

We get rid of parentheses

-4x-18/5x+9=0

We multiply all the terms by the denominator


-4x*5x+9*5x-18=0

Wy multiply elements

-20x^2+45x-18=0

a = -20; b = 45; c = -18;
Δ = b2-4ac
Δ = 452-4·(-20)·(-18)
Δ = 585
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:

$\sqrt{\Delta}=\sqrt{585}=\sqrt{9*65}=\sqrt{9}*\sqrt{65}=3\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-3\sqrt{65}}{2*-20}=\frac{-45-3\sqrt{65}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+3\sqrt{65}}{2*-20}=\frac{-45+3\sqrt{65}}{-40}
$