1/2x+1/4=1/4x-6

Solution for 1/2x+1/4=1/4x-6 equation:

1/2x+1/4=1/4x-6

We move all terms to the left:

1/2x+1/4-(1/4x-6)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x-6)!=0

x∈R


We get rid of parentheses

1/2x-1/4x+6+1/4=0

We calculate fractions


64x/128x^2+(-2x)/128x^2+2x/128x^2+6=0

We multiply all the terms by the denominator


64x+(-2x)+2x+6*128x^2=0

We add all the numbers together, and all the variables

66x+(-2x)+6*128x^2=0

Wy multiply elements

768x^2+66x+(-2x)=0

We get rid of parentheses

768x^2+66x-2x=0

We add all the numbers together, and all the variables

768x^2+64x=0

a = 768; b = 64; c = 0;
Δ = b2-4ac
Δ = 642-4·768·0
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-64}{2*768}=\frac{-128}{1536}
=-1/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+64}{2*768}=\frac{0}{1536}
=0
$