(-2x+1)-(6x-4)x=-2

Solution for (-2x+1)-(6x-4)x=-2 equation:

(-2x+1)-(6x-4)x=-2

We move all terms to the left:

(-2x+1)-(6x-4)x-(-2)=0

We add all the numbers together, and all the variables

(-2x+1)-(6x-4)x+2=0

We multiply parentheses

-6x^2+(-2x+1)+4x+2=0

We get rid of parentheses

-6x^2-2x+4x+1+2=0

We add all the numbers together, and all the variables

-6x^2+2x+3=0

a = -6; b = 2; c = +3;
Δ = b2-4ac
Δ = 22-4·(-6)·3
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{19}}{2*-6}=\frac{-2-2\sqrt{19}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{19}}{2*-6}=\frac{-2+2\sqrt{19}}{-12}
$