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

Solution for 5/2x-1x=3+3/2x equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

a = -2; b = -6; c = +2;
Δ = b2-4ac
Δ = -62-4·(-2)·2
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{13}}{2*-2}=\frac{6-2\sqrt{13}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{13}}{2*-2}=\frac{6+2\sqrt{13}}{-4}
$