2x-1=2/4x+9

Solution for 2x-1=2/4x+9 equation:

2x-1=2/4x+9

We move all terms to the left:

2x-1-(2/4x+9)=0


Domain of the equation: 4x+9)!=0

x∈R


We get rid of parentheses

2x-2/4x-9-1=0

We multiply all the terms by the denominator


2x*4x-9*4x-1*4x-2=0

Wy multiply elements

8x^2-36x-4x-2=0

We add all the numbers together, and all the variables

8x^2-40x-2=0

a = 8; b = -40; c = -2;
Δ = b2-4ac
Δ = -402-4·8·(-2)
Δ = 1664
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:

$\sqrt{\Delta}=\sqrt{1664}=\sqrt{64*26}=\sqrt{64}*\sqrt{26}=8\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-8\sqrt{26}}{2*8}=\frac{40-8\sqrt{26}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+8\sqrt{26}}{2*8}=\frac{40+8\sqrt{26}}{16}
$