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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

8x+(-64x)-2*128x^2=0

Wy multiply elements

-256x^2+8x+(-64x)=0

We get rid of parentheses

-256x^2+8x-64x=0

We add all the numbers together, and all the variables

-256x^2-56x=0

a = -256; b = -56; c = 0;
Δ = b2-4ac
Δ = -562-4·(-256)·0
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-56}{2*-256}=\frac{0}{-512}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+56}{2*-256}=\frac{112}{-512}
=-7/32
$