5/2x-x+2=3+3/2x

Solution for 5/2x-x+2=3+3/2x equation:

5/2x-x+2=3+3/2x

We move all terms to the left:

5/2x-x+2-(3+3/2x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5/2x-x-(3/2x+3)+2=0

We add all the numbers together, and all the variables

-1x+5/2x-(3/2x+3)+2=0

We get rid of parentheses

-1x+5/2x-3/2x-3+2=0

We multiply all the terms by the denominator


-1x*2x-3*2x+2*2x+5-3=0

We add all the numbers together, and all the variables

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

Wy multiply elements

-2x^2-6x+4x+2=0

We add all the numbers together, and all the variables

-2x^2-2x+2=0

a = -2; b = -2; c = +2;
Δ = b2-4ac
Δ = -22-4·(-2)·2
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{5}}{2*-2}=\frac{2-2\sqrt{5}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{5}}{2*-2}=\frac{2+2\sqrt{5}}{-4}
$