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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

11x^2-22x+2x-6+2=0

We add all the numbers together, and all the variables

11x^2-20x-4=0

a = 11; b = -20; c = -4;
Δ = b2-4ac
Δ = -202-4·11·(-4)
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{-(-20)-24}{2*11}=\frac{-4}{22}
=-2/11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+24}{2*11}=\frac{44}{22}
=2
$