X(x+5)=2x(x+1)

Solution for X(x+5)=2x(x+1) equation:

X(X+5)=2X(X+1)

We move all terms to the left:

X(X+5)-(2X(X+1))=0

We multiply parentheses

X^2+5X-(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+5X-2X=0

We add all the numbers together, and all the variables

-1X^2+3X=0

a = -1; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-1)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-1}=\frac{-6}{-2}
=+3
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-1}=\frac{0}{-2}
=0
$