2x-1=1/4x-2

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

2x-1=1/4x-2

We move all terms to the left:

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


Domain of the equation: 4x-2)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

8x^2+4x-1=0

a = 8; b = 4; c = -1;
Δ = b2-4ac
Δ = 42-4·8·(-1)
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{3}}{2*8}=\frac{-4-4\sqrt{3}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{3}}{2*8}=\frac{-4+4\sqrt{3}}{16}
$