3(x+6)-4=6x2

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

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

We move all terms to the left:

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

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

We multiply parentheses

-6x^2+3x+18-4=0

We add all the numbers together, and all the variables

-6x^2+3x+14=0

a = -6; b = 3; c = +14;
Δ = b2-4ac
Δ = 32-4·(-6)·14
Δ = 345
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{345}}{2*-6}=\frac{-3-\sqrt{345}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{345}}{2*-6}=\frac{-3+\sqrt{345}}{-12}
$