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

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

X(X+3)=2X(X-1)

We move all terms to the left:

X(X+3)-(2X(X-1))=0

We multiply parentheses

X^2+3X-(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

X^2-2X^2+3X+2X=0

We add all the numbers together, and all the variables

-1X^2+5X=0

a = -1; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-1)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-1}=\frac{-10}{-2}
=+5
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-1}=\frac{0}{-2}
=0
$