4+6x=2(3x2)

Solution for 4+6x=2(3x2) equation:

4+6x=2(3x^2)

We move all terms to the left:

4+6x-(2(3x^2))=0

determiningTheFunctionDomain
6x-23x^2+4=0

We add all the numbers together, and all the variables

-23x^2+6x+4=0

a = -23; b = 6; c = +4;
Δ = b2-4ac
Δ = 62-4·(-23)·4
Δ = 404
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:

$\sqrt{\Delta}=\sqrt{404}=\sqrt{4*101}=\sqrt{4}*\sqrt{101}=2\sqrt{101}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{101}}{2*-23}=\frac{-6-2\sqrt{101}}{-46}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{101}}{2*-23}=\frac{-6+2\sqrt{101}}{-46}
$