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

Solution for 1-4x+4x^2/1-2x+x/1-2x=0 equation:

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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

We add all the numbers together, and all the variables

4x^2-7x+1=0

a = 4; b = -7; c = +1;
Δ = b2-4ac
Δ = -72-4·4·1
Δ = 33
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{-(-7)-\sqrt{33}}{2*4}=\frac{7-\sqrt{33}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{33}}{2*4}=\frac{7+\sqrt{33}}{8}
$