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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

2x-(x+6)/2x-4=0

We multiply all the terms by the denominator


2x*2x-(x+6)-4*2x=0

Wy multiply elements

4x^2-(x+6)-8x=0

We get rid of parentheses

4x^2-x-8x-6=0

We add all the numbers together, and all the variables

4x^2-9x-6=0

a = 4; b = -9; c = -6;
Δ = b2-4ac
Δ = -92-4·4·(-6)
Δ = 177
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{-(-9)-\sqrt{177}}{2*4}=\frac{9-\sqrt{177}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{177}}{2*4}=\frac{9+\sqrt{177}}{8}
$