3x+2.3-1/2x=4.3+x

Solution for 3x+2.3-1/2x=4.3+x equation:

3x+2.3-1/2x=4.3+x

We move all terms to the left:

3x+2.3-1/2x-(4.3+x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3x-1/2x-(x+4.3)+2.3=0

We get rid of parentheses

3x-1/2x-x-4.3+2.3=0

We multiply all the terms by the denominator


3x*2x-x*2x-(4.3)*2x+(2.3)*2x-1=0

We multiply parentheses

3x*2x-x*2x-8.6x+4.6x-1=0

Wy multiply elements

6x^2-2x^2-8.6x+4.6x-1=0

We add all the numbers together, and all the variables

4x^2-4x-1=0

a = 4; b = -4; c = -1;
Δ = b2-4ac
Δ = -42-4·4·(-1)
Δ = 32
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{2}}{2*4}=\frac{4-4\sqrt{2}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{2}}{2*4}=\frac{4+4\sqrt{2}}{8}
$