12-6x=2(5x2)

Solution for 12-6x=2(5x2) equation:

12-6x=2(5x^2)

We move all terms to the left:

12-6x-(2(5x^2))=0

determiningTheFunctionDomain
-6x-25x^2+12=0

We add all the numbers together, and all the variables

-25x^2-6x+12=0

a = -25; b = -6; c = +12;
Δ = b2-4ac
Δ = -62-4·(-25)·12
Δ = 1236
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:

$\sqrt{\Delta}=\sqrt{1236}=\sqrt{4*309}=\sqrt{4}*\sqrt{309}=2\sqrt{309}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{309}}{2*-25}=\frac{6-2\sqrt{309}}{-50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{309}}{2*-25}=\frac{6+2\sqrt{309}}{-50}
$