3=2x(X-1)

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

3=2x(x-1)

We move all terms to the left:

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


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

2x(x-1)

We multiply parentheses

2x^2-2x

Back to the equation:

-(2x^2-2x)


We get rid of parentheses

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

a = -2; b = 2; c = +3;
Δ = b2-4ac
Δ = 22-4·(-2)·3
Δ = 28
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{7}}{2*-2}=\frac{-2-2\sqrt{7}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{7}}{2*-2}=\frac{-2+2\sqrt{7}}{-4}
$