2x+5/x+9=1

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

2x+5/x+9=1

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

2x+5/x+8=0

We multiply all the terms by the denominator


2x*x+8*x+5=0

We add all the numbers together, and all the variables

8x+2x*x+5=0

Wy multiply elements

2x^2+8x+5=0

a = 2; b = 8; c = +5;
Δ = b2-4ac
Δ = 82-4·2·5
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{6}}{2*2}=\frac{-8-2\sqrt{6}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{6}}{2*2}=\frac{-8+2\sqrt{6}}{4}
$