31/2x+2.3-11/2X=4.3+X

Solution for 31/2x+2.3-11/2X=4.3+X equation:

31/2x+2.3-11/2x=4.3+x

We move all terms to the left:

31/2x+2.3-11/2x-(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

31/2x-11/2x-(x+4.3)+2.3=0

We get rid of parentheses

31/2x-11/2x-x-4.3+2.3=0

We multiply all the terms by the denominator


-x*2x-(4.3)*2x+(2.3)*2x+31-11=0

We add all the numbers together, and all the variables

-x*2x-(4.3)*2x+(2.3)*2x+20=0

We multiply parentheses

-x*2x-8.6x+4.6x+20=0

Wy multiply elements

-2x^2-8.6x+4.6x+20=0

We add all the numbers together, and all the variables

-2x^2-4x+20=0

a = -2; b = -4; c = +20;
Δ = b2-4ac
Δ = -42-4·(-2)·20
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{11}}{2*-2}=\frac{4-4\sqrt{11}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{11}}{2*-2}=\frac{4+4\sqrt{11}}{-4}
$