2x-1=1/4x+9

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

2x-1=1/4x+9

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

8x^2-36x-4x-1=0

We add all the numbers together, and all the variables

8x^2-40x-1=0

a = 8; b = -40; c = -1;
Δ = b2-4ac
Δ = -402-4·8·(-1)
Δ = 1632
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:

$\sqrt{\Delta}=\sqrt{1632}=\sqrt{16*102}=\sqrt{16}*\sqrt{102}=4\sqrt{102}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-4\sqrt{102}}{2*8}=\frac{40-4\sqrt{102}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+4\sqrt{102}}{2*8}=\frac{40+4\sqrt{102}}{16}
$