2x(4-3x)=2

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

2x(4-3x)=2

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

a = -6; b = 8; c = -2;
Δ = b2-4ac
Δ = 82-4·(-6)·(-2)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4}{2*-6}=\frac{-12}{-12}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4}{2*-6}=\frac{-4}{-12}
=1/3
$