392-2x=6x^2

Solution for 392-2x=6x^2 equation:

392-2x=6x^2

We move all terms to the left:

392-2x-(6x^2)=0

determiningTheFunctionDomain
-6x^2-2x+392=0

a = -6; b = -2; c = +392;
Δ = b2-4ac
Δ = -22-4·(-6)·392
Δ = 9412
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:

$\sqrt{\Delta}=\sqrt{9412}=\sqrt{4*2353}=\sqrt{4}*\sqrt{2353}=2\sqrt{2353}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{2353}}{2*-6}=\frac{2-2\sqrt{2353}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{2353}}{2*-6}=\frac{2+2\sqrt{2353}}{-12}
$