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

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

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

We move all terms to the left:

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


Domain of the equation: 2x*3!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


4x/96x^2+54x/96x^2-2=0

We multiply all the terms by the denominator


4x+54x-2*96x^2=0

We add all the numbers together, and all the variables

58x-2*96x^2=0

Wy multiply elements

-192x^2+58x=0

a = -192; b = 58; c = 0;
Δ = b2-4ac
Δ = 582-4·(-192)·0
Δ = 3364
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3364}=58$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(58)-58}{2*-192}=\frac{-116}{-384}
=29/96
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(58)+58}{2*-192}=\frac{0}{-384}
=0
$