2x(3x+1)=13

Solution for 2x(3x+1)=13 equation:

2x(3x+1)=13

We move all terms to the left:

2x(3x+1)-(13)=0

We multiply parentheses

6x^2+2x-13=0

a = 6; b = 2; c = -13;
Δ = b2-4ac
Δ = 22-4·6·(-13)
Δ = 316
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:

$\sqrt{\Delta}=\sqrt{316}=\sqrt{4*79}=\sqrt{4}*\sqrt{79}=2\sqrt{79}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{79}}{2*6}=\frac{-2-2\sqrt{79}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{79}}{2*6}=\frac{-2+2\sqrt{79}}{12}
$