2x+x-3x2-x=-6

Solution for 2x+x-3x2-x=-6 equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

a = -3; b = 2; c = +6;
Δ = b2-4ac
Δ = 22-4·(-3)·6
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*-3}=\frac{-2-2\sqrt{19}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{19}}{2*-3}=\frac{-2+2\sqrt{19}}{-6}
$