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

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

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

We move all terms to the left:

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

We calculate fractions


(-24x)/32x^2+(-12x)/32x^2+4x/32x^2+1=0

We multiply all the terms by the denominator


(-24x)+(-12x)+4x+1*32x^2=0

We add all the numbers together, and all the variables

4x+(-24x)+(-12x)+1*32x^2=0

Wy multiply elements

32x^2+4x+(-24x)+(-12x)=0

We get rid of parentheses

32x^2+4x-24x-12x=0

We add all the numbers together, and all the variables

32x^2-32x=0

a = 32; b = -32; c = 0;
Δ = b2-4ac
Δ = -322-4·32·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-32}{2*32}=\frac{0}{64}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+32}{2*32}=\frac{64}{64}
=1
$