12=3x^2+4x-1

Solution for 12=3x^2+4x-1 equation:

12=3x^2+4x-1

We move all terms to the left:

12-(3x^2+4x-1)=0

We get rid of parentheses

-3x^2-4x+1+12=0

We add all the numbers together, and all the variables

-3x^2-4x+13=0

a = -3; b = -4; c = +13;
Δ = b2-4ac
Δ = -42-4·(-3)·13
Δ = 172
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:

$\sqrt{\Delta}=\sqrt{172}=\sqrt{4*43}=\sqrt{4}*\sqrt{43}=2\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{43}}{2*-3}=\frac{4-2\sqrt{43}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{43}}{2*-3}=\frac{4+2\sqrt{43}}{-6}
$