x2-x+1/4=x/4

Solution for x2-x+1/4=x/4 equation:

x2-x+1/4=x/4

We move all terms to the left:

x2-x+1/4-(x/4)=0

We add all the numbers together, and all the variables

x2-x-(+x/4)+1/4=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

We add all the numbers together, and all the variables

4x^2-5x+1=0

a = 4; b = -5; c = +1;
Δ = b2-4ac
Δ = -52-4·4·1
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3}{2*4}=\frac{2}{8}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3}{2*4}=\frac{8}{8}
=1
$