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

Solution for 2x(3x-1)+3(3x-1)+4=0 equation:

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

We multiply parentheses

6x^2-2x+9x-3+4=0

We add all the numbers together, and all the variables

6x^2+7x+1=0

a = 6; b = 7; c = +1;
Δ = b2-4ac
Δ = 72-4·6·1
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-5}{2*6}=\frac{-12}{12}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+5}{2*6}=\frac{-2}{12}
=-1/6
$