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

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

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

We move all terms to the left:

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

We multiply parentheses

6x^2-2x-(4(2x+1))=0


We calculate terms in parentheses: -(4(2x+1)), so:

4(2x+1)

We multiply parentheses

8x+4

Back to the equation:

-(8x+4)


We get rid of parentheses

6x^2-2x-8x-4=0

We add all the numbers together, and all the variables

6x^2-10x-4=0

a = 6; b = -10; c = -4;
Δ = b2-4ac
Δ = -102-4·6·(-4)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-14}{2*6}=\frac{-4}{12}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+14}{2*6}=\frac{24}{12}
=2
$