1.5x(2-4x)=6x

Solution for 1.5x(2-4x)=6x equation:

1.5x(2-4x)=6x

We move all terms to the left:

1.5x(2-4x)-(6x)=0

We add all the numbers together, and all the variables

1.5x(-4x+2)-6x=0

We add all the numbers together, and all the variables

-6x+1.5x(-4x+2)=0

We multiply parentheses

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

We add all the numbers together, and all the variables

-4x^2-4x=0

a = -4; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-4)·0
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{-(-4)-4}{2*-4}=\frac{0}{-8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-4}=\frac{8}{-8}
=-1
$