2x+9=(1/5x)

Solution for 2x+9=(1/5x) equation:

2x+9=(1/5x)

We move all terms to the left:

2x+9-((1/5x))=0


Domain of the equation: 5x))!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x-((+1/5x))+9=0

We multiply all the terms by the denominator


2x*5x))-((+9*5x))+1=0

Wy multiply elements

10x^2+45x=0

a = 10; b = 45; c = 0;
Δ = b2-4ac
Δ = 452-4·10·0
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-45}{2*10}=\frac{-90}{20}
=-4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+45}{2*10}=\frac{0}{20}
=0
$