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 get rid of parentheses

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-1=0

a = 10; b = 45; c = -1;
Δ = b2-4ac
Δ = 452-4·10·(-1)
Δ = 2065
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-\sqrt{2065}}{2*10}=\frac{-45-\sqrt{2065}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+\sqrt{2065}}{2*10}=\frac{-45+\sqrt{2065}}{20}
$