3/2x+2.3-1/2x=4/3+x

Solution for 3/2x+2.3-1/2x=4/3+x equation:

3/2x+2.3-1/2x=4/3+x

We move all terms to the left:

3/2x+2.3-1/2x-(4/3+x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3+x)!=0

We move all terms containing x to the left, all other terms to the right

x)!=-3

x!=-3/1

x!=-3

x∈R


We add all the numbers together, and all the variables

3/2x-1/2x-(+x+4/3)+2.3=0

We get rid of parentheses

3/2x-1/2x-x+2.3-4/3=0

We calculate fractions


-x+()/6x+(-8x)/6x+2.3=0

We add all the numbers together, and all the variables

-1x+()/6x+(-8x)/6x+2.3=0

We multiply all the terms by the denominator


-1x*6x+(-8x)+(2.3)*6x+()=0

We add all the numbers together, and all the variables

-1x*6x+(-8x)+(2.3)*6x=0

We multiply parentheses

-1x*6x+(-8x)+13.8x=0

Wy multiply elements

-6x^2+(-8x)+13.8x=0

We get rid of parentheses

-6x^2-8x+13.8x=0

We add all the numbers together, and all the variables

-6x^2+5.8x=0

a = -6; b = 5.8; c = 0;
Δ = b2-4ac
Δ = 5.82-4·(-6)·0
Δ = 33.64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5.8)-\sqrt{33.64}}{2*-6}=\frac{-5.8-\sqrt{33.64}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5.8)+\sqrt{33.64}}{2*-6}=\frac{-5.8+\sqrt{33.64}}{-12}
$