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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x+1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


6x/128x^2+(-64x)/128x^2+(-2x)/128x^2-1-4=0

We add all the numbers together, and all the variables

6x/128x^2+(-64x)/128x^2+(-2x)/128x^2-5=0

We multiply all the terms by the denominator


6x+(-64x)+(-2x)-5*128x^2=0

Wy multiply elements

-640x^2+6x+(-64x)+(-2x)=0

We get rid of parentheses

-640x^2+6x-64x-2x=0

We add all the numbers together, and all the variables

-640x^2-60x=0

a = -640; b = -60; c = 0;
Δ = b2-4ac
Δ = -602-4·(-640)·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*-640}=\frac{0}{-1280}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+60}{2*-640}=\frac{120}{-1280}
=-3/32
$