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

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

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

We move all terms to the left:

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

We multiply parentheses

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


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

2X(X-3)

We multiply parentheses

2X^2-6X

Back to the equation:

-(2X^2-6X)


We get rid of parentheses

X^2-2X^2+X+6X=0

We add all the numbers together, and all the variables

-1X^2+7X=0

a = -1; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-1)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-1}=\frac{-14}{-2}
=+7
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-1}=\frac{0}{-2}
=0
$