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

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

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

We move all terms to the left:

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

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

We calculate fractions


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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

28x+(-12x)-2*32x^2=0

Wy multiply elements

-64x^2+28x+(-12x)=0

We get rid of parentheses

-64x^2+28x-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{-32}{-128}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*-64}=\frac{0}{-128}
=0
$