2x/x-3-1/2=2/2x-6

Solution for 2x/x-3-1/2=2/2x-6 equation:

2x/x-3-1/2=2/2x-6

We move all terms to the left:

2x/x-3-1/2-(2/2x-6)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x-6)!=0

x∈R


We get rid of parentheses

2x/x-2/2x+6-3-1/2=0

We calculate fractions


16x^2/8x^2+(-2x)/8x^2+(-x)/8x^2+6-3=0

We add all the numbers together, and all the variables

16x^2/8x^2+(-2x)/8x^2+(-1x)/8x^2+6-3=0

We add all the numbers together, and all the variables

16x^2/8x^2+(-2x)/8x^2+(-1x)/8x^2+3=0

We multiply all the terms by the denominator


16x^2+(-2x)+(-1x)+3*8x^2=0

Wy multiply elements

16x^2+24x^2+(-2x)+(-1x)=0

We get rid of parentheses

16x^2+24x^2-2x-1x=0

We add all the numbers together, and all the variables

40x^2-3x=0

a = 40; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·40·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*40}=\frac{0}{80}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*40}=\frac{6}{80}
=3/40
$