2x-4x(3+2x)+6+(x-2)=0

Solution for 2x-4x(3+2x)+6+(x-2)=0 equation:

2x-4x(3+2x)+6+(x-2)=0

We add all the numbers together, and all the variables

2x-4x(2x+3)+(x-2)+6=0

We multiply parentheses

-8x^2+2x-12x+(x-2)+6=0

We get rid of parentheses

-8x^2+2x-12x+x-2+6=0

We add all the numbers together, and all the variables

-8x^2-9x+4=0

a = -8; b = -9; c = +4;
Δ = b2-4ac
Δ = -92-4·(-8)·4
Δ = 209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{209}}{2*-8}=\frac{9-\sqrt{209}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{209}}{2*-8}=\frac{9+\sqrt{209}}{-16}
$