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

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

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

We move all terms to the left:

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

We multiply parentheses

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


We calculate terms in parentheses: -(3x(x-1)), so:

3x(x-1)

We multiply parentheses

3x^2-3x

Back to the equation:

-(3x^2-3x)


We get rid of parentheses

2x^2-3x^2+2x+3x=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
$