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

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

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

We move all terms to the left:

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

We multiply parentheses

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


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

2(x-3)

We multiply parentheses

2x-6

Back to the equation:

-(2x-6)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-2x^2+6=0

a = -2; b = 0; c = +6;
Δ = b2-4ac
Δ = 02-4·(-2)·6
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{3}}{2*-2}=\frac{0-4\sqrt{3}}{-4}
=-\frac{4\sqrt{3}}{-4}
=-\frac{\sqrt{3}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{3}}{2*-2}=\frac{0+4\sqrt{3}}{-4}
=\frac{4\sqrt{3}}{-4}
=\frac{\sqrt{3}}{-1}
$