1/4x-0,25=x+0,5

Solution for 1/4x-0,25=x+0,5 equation:

1/4x-0.25=x+0.5

We move all terms to the left:

1/4x-0.25-(x+0.5)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

1/4x-x-0.5-0.25=0

We multiply all the terms by the denominator


-x*4x-(0.5)*4x-(0.25)*4x+1=0

We multiply parentheses

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

Wy multiply elements

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

We add all the numbers together, and all the variables

-4x^2-3x+1=0

a = -4; b = -3; c = +1;
Δ = b2-4ac
Δ = -32-4·(-4)·1
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-5}{2*-4}=\frac{-2}{-8}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+5}{2*-4}=\frac{8}{-8}
=-1
$