x/x-3=2x-11/2x

Solution for x/x-3=2x-11/2x equation:

x/x-3=2x-11/2x

We move all terms to the left:

x/x-3-(2x-11/2x)=0


Domain of the equation: 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

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

We get rid of parentheses

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

Fractions to decimals

11/2x-2x-3+1=0

We multiply all the terms by the denominator


-2x*2x-3*2x+1*2x+11=0

Wy multiply elements

-4x^2-6x+2x+11=0

We add all the numbers together, and all the variables

-4x^2-4x+11=0

a = -4; b = -4; c = +11;
Δ = b2-4ac
Δ = -42-4·(-4)·11
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-8\sqrt{3}}{2*-4}=\frac{4-8\sqrt{3}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8\sqrt{3}}{2*-4}=\frac{4+8\sqrt{3}}{-8}
$