x(3x+1)=12

Solution for x(3x+1)=12 equation:

x(3x+1)=12

We move all terms to the left:

x(3x+1)-(12)=0

We multiply parentheses

3x^2+x-12=0

a = 3; b = 1; c = -12;
Δ = b2-4ac
Δ = 12-4·3·(-12)
Δ = 145
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{-(1)-\sqrt{145}}{2*3}=\frac{-1-\sqrt{145}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{145}}{2*3}=\frac{-1+\sqrt{145}}{6}
$