3(2x-1)=8x(x-1)

Solution for 3(2x-1)=8x(x-1) equation:

3(2x-1)=8x(x-1)

We move all terms to the left:

3(2x-1)-(8x(x-1))=0

We multiply parentheses

6x-(8x(x-1))-3=0


We calculate terms in parentheses: -(8x(x-1)), so:

8x(x-1)

We multiply parentheses

8x^2-8x

Back to the equation:

-(8x^2-8x)


We get rid of parentheses

-8x^2+6x+8x-3=0

We add all the numbers together, and all the variables

-8x^2+14x-3=0

a = -8; b = 14; c = -3;
Δ = b2-4ac
Δ = 142-4·(-8)·(-3)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-10}{2*-8}=\frac{-24}{-16}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+10}{2*-8}=\frac{-4}{-16}
=1/4
$