x+11/2x-5=2

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

x+11/2x-5=2

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

x+11/2x-7=0

We multiply all the terms by the denominator


x*2x-7*2x+11=0

Wy multiply elements

2x^2-14x+11=0

a = 2; b = -14; c = +11;
Δ = b2-4ac
Δ = -142-4·2·11
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-6\sqrt{3}}{2*2}=\frac{14-6\sqrt{3}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+6\sqrt{3}}{2*2}=\frac{14+6\sqrt{3}}{4}
$