X(2x-1)=x-2(x-2)

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

X(2X-1)=X-2(X-2)

We move all terms to the left:

X(2X-1)-(X-2(X-2))=0

We multiply parentheses

2X^2-1X-(X-2(X-2))=0


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

X-2(X-2)

We multiply parentheses

X-2X+4

We add all the numbers together, and all the variables

-1X+4

Back to the equation:

-(-1X+4)


We get rid of parentheses

2X^2-1X+1X-4=0

We add all the numbers together, and all the variables

2X^2-4=0

a = 2; b = 0; c = -4;
Δ = b2-4ac
Δ = 02-4·2·(-4)
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{2}}{2*2}=\frac{0-4\sqrt{2}}{4}
=-\frac{4\sqrt{2}}{4}
=-\sqrt{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{2}}{2*2}=\frac{0+4\sqrt{2}}{4}
=\frac{4\sqrt{2}}{4}
=\sqrt{2}
$