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

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

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

We move all terms to the left:

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

We multiply parentheses

5x^2+10x-(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

5x^2-2x^2+10x-2x=0

We add all the numbers together, and all the variables

3x^2+8x=0

a = 3; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·3·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*3}=\frac{-16}{6}
=-2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*3}=\frac{0}{6}
=0
$