x^2/2-1/2-11x=11

Solution for x^2/2-1/2-11x=11 equation:

x^2/2-1/2-11x=11

We move all terms to the left:

x^2/2-1/2-11x-(11)=0

determiningTheFunctionDomain
x^2/2-11x-11-1/2=0

We multiply all the terms by the denominator


x^2-11x*2-1-11*2=0

We add all the numbers together, and all the variables

x^2-11x*2-23=0

Wy multiply elements

x^2-22x-23=0

a = 1; b = -22; c = -23;
Δ = b2-4ac
Δ = -222-4·1·(-23)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-24}{2*1}=\frac{-2}{2}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+24}{2*1}=\frac{46}{2}
=23
$