1/4+1/4x=1/2x-3

Solution for 1/4+1/4x=1/2x-3 equation:

1/4+1/4x=1/2x-3

We move all terms to the left:

1/4+1/4x-(1/2x-3)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x-3)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


2x/128x^2+(-64x)/128x^2+2x/128x^2+3=0

We multiply all the terms by the denominator


2x+(-64x)+2x+3*128x^2=0

We add all the numbers together, and all the variables

4x+(-64x)+3*128x^2=0

Wy multiply elements

384x^2+4x+(-64x)=0

We get rid of parentheses

384x^2+4x-64x=0

We add all the numbers together, and all the variables

384x^2-60x=0

a = 384; b = -60; c = 0;
Δ = b2-4ac
Δ = -602-4·384·0
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-60}{2*384}=\frac{0}{768}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+60}{2*384}=\frac{120}{768}
=5/32
$