11/2x-5=x

Solution for 11/2x-5=x equation:

11/2x-5=x

We move all terms to the left:

11/2x-5-(x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+11/2x-5=0

We multiply all the terms by the denominator


-1x*2x-5*2x+11=0

Wy multiply elements

-2x^2-10x+11=0

a = -2; b = -10; c = +11;
Δ = b2-4ac
Δ = -102-4·(-2)·11
Δ = 188
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:

$\sqrt{\Delta}=\sqrt{188}=\sqrt{4*47}=\sqrt{4}*\sqrt{47}=2\sqrt{47}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{47}}{2*-2}=\frac{10-2\sqrt{47}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{47}}{2*-2}=\frac{10+2\sqrt{47}}{-4}
$