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

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

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

We move all terms to the left:

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

We multiply parentheses

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


We calculate terms in parentheses: -(3(2x-1)), so:

3(2x-1)

We multiply parentheses

6x-3

Back to the equation:

-(6x-3)


We get rid of parentheses

8x^2-8x-6x+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{4}{16}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+10}{2*8}=\frac{24}{16}
=1+1/2
$