1/4x-1/2x+5/4x=1-2

Solution for 1/4x-1/2x+5/4x=1-2 equation:

1/4x-1/2x+5/4x=1-2

We move all terms to the left:

1/4x-1/2x+5/4x-(1-2)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

1/4x-1/2x+5/4x-(-1)=0

We add all the numbers together, and all the variables

1/4x-1/2x+5/4x+1=0

We calculate fractions


(10x+1)/8x^2+(-4x)/8x^2+1=0

We multiply all the terms by the denominator


(10x+1)+(-4x)+1*8x^2=0

Wy multiply elements

8x^2+(10x+1)+(-4x)=0

We get rid of parentheses

8x^2+10x-4x+1=0

We add all the numbers together, and all the variables

8x^2+6x+1=0

a = 8; b = 6; c = +1;
Δ = b2-4ac
Δ = 62-4·8·1
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2}{2*8}=\frac{-8}{16}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2}{2*8}=\frac{-4}{16}
=-1/4
$