3x(2x-1)=13

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

3x(2x-1)=13

We move all terms to the left:

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

We multiply parentheses

6x^2-3x-13=0

a = 6; b = -3; c = -13;
Δ = b2-4ac
Δ = -32-4·6·(-13)
Δ = 321
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{321}}{2*6}=\frac{3-\sqrt{321}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{321}}{2*6}=\frac{3+\sqrt{321}}{12}
$