1/2x+4.3=2.1-1x

Solution for 1/2x+4.3=2.1-1x equation:

1/2x+4.3=2.1-1x

We move all terms to the left:

1/2x+4.3-(2.1-1x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-(-1x+2.1)+4.3=0

We get rid of parentheses

1/2x+1x-2.1+4.3=0

We multiply all the terms by the denominator


1x*2x-(2.1)*2x+(4.3)*2x+1=0

We multiply parentheses

1x*2x-4.2x+8.6x+1=0

Wy multiply elements

2x^2-4.2x+8.6x+1=0

We add all the numbers together, and all the variables

2x^2+4.4x+1=0

a = 2; b = 4.4; c = +1;
Δ = b2-4ac
Δ = 4.42-4·2·1
Δ = 11.36
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{-(4.4)-\sqrt{11.36}}{2*2}=\frac{-4.4-\sqrt{11.36}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4.4)+\sqrt{11.36}}{2*2}=\frac{-4.4+\sqrt{11.36}}{4}
$