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

Solution for (x/2)+2=11/(3-x) equation:

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

We move all terms to the left:

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


Domain of the equation: (3-x))!=0

We move all terms containing x to the left, all other terms to the right

-x)!=-3

x!=-3/1

x!=-3

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


2x^2/(-2x)+()/(-2x)+2=0

We multiply all the terms by the denominator


2x^2+2*(-2x)+()=0

We add all the numbers together, and all the variables

2x^2+2*(-2x)=0

We multiply parentheses

2x^2-4x=0

a = 2; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·2·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*2}=\frac{8}{4}
=2
$