3/x-3+5/2x-6=11/2

Solution for 3/x-3+5/2x-6=11/2 equation:

3/x-3+5/2x-6=11/2

We move all terms to the left:

3/x-3+5/2x-6-(11/2)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3/x+5/2x-3-6-(+11/2)=0

We add all the numbers together, and all the variables

3/x+5/2x-9-(+11/2)=0

We get rid of parentheses

3/x+5/2x-9-11/2=0

We calculate fractions


24x/8x^2+5x/8x^2+(-11x)/8x^2-9=0

We multiply all the terms by the denominator


24x+5x+(-11x)-9*8x^2=0

We add all the numbers together, and all the variables

29x+(-11x)-9*8x^2=0

Wy multiply elements

-72x^2+29x+(-11x)=0

We get rid of parentheses

-72x^2+29x-11x=0

We add all the numbers together, and all the variables

-72x^2+18x=0

a = -72; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·(-72)·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*-72}=\frac{-36}{-144}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*-72}=\frac{0}{-144}
=0
$