3(x-2)=4x(4x-8)

Solution for 3(x-2)=4x(4x-8) equation:

3(x-2)=4x(4x-8)

We move all terms to the left:

3(x-2)-(4x(4x-8))=0

We multiply parentheses

3x-(4x(4x-8))-6=0


We calculate terms in parentheses: -(4x(4x-8)), so:

4x(4x-8)

We multiply parentheses

16x^2-32x

Back to the equation:

-(16x^2-32x)


We get rid of parentheses

-16x^2+3x+32x-6=0

We add all the numbers together, and all the variables

-16x^2+35x-6=0

a = -16; b = 35; c = -6;
Δ = b2-4ac
Δ = 352-4·(-16)·(-6)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-29}{2*-16}=\frac{-64}{-32}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+29}{2*-16}=\frac{-6}{-32}
=3/16
$