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

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

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

We move all terms to the left:

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

We multiply parentheses

6x^2-3x-(2x+13)=0

We get rid of parentheses

6x^2-3x-2x-13=0

We add all the numbers together, and all the variables

6x^2-5x-13=0

a = 6; b = -5; c = -13;
Δ = b2-4ac
Δ = -52-4·6·(-13)
Δ = 337
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{-(-5)-\sqrt{337}}{2*6}=\frac{5-\sqrt{337}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{337}}{2*6}=\frac{5+\sqrt{337}}{12}
$