2x(31-3x)=-6

Solution for 2x(31-3x)=-6 equation:

2x(31-3x)=-6

We move all terms to the left:

2x(31-3x)-(-6)=0

We add all the numbers together, and all the variables

2x(-3x+31)-(-6)=0

We add all the numbers together, and all the variables

2x(-3x+31)+6=0

We multiply parentheses

-6x^2+62x+6=0

a = -6; b = 62; c = +6;
Δ = b2-4ac
Δ = 622-4·(-6)·6
Δ = 3988
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:

$\sqrt{\Delta}=\sqrt{3988}=\sqrt{4*997}=\sqrt{4}*\sqrt{997}=2\sqrt{997}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(62)-2\sqrt{997}}{2*-6}=\frac{-62-2\sqrt{997}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(62)+2\sqrt{997}}{2*-6}=\frac{-62+2\sqrt{997}}{-12}
$