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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


4x/32x^2+(-8x)/32x^2+(-12x)/32x^2+2=0

We multiply all the terms by the denominator


4x+(-8x)+(-12x)+2*32x^2=0

Wy multiply elements

64x^2+4x+(-8x)+(-12x)=0

We get rid of parentheses

64x^2+4x-8x-12x=0

We add all the numbers together, and all the variables

64x^2-16x=0

a = 64; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·64·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16}{2*64}=\frac{0}{128}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*64}=\frac{32}{128}
=1/4
$