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

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

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

We move all terms to the left:

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

We multiply parentheses

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


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

-2x(x-2)

We multiply parentheses

-2x^2+4x

Back to the equation:

-(-2x^2+4x)


We get rid of parentheses

5x^2+2x^2-4x+5x=0

We add all the numbers together, and all the variables

7x^2+x=0

a = 7; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·7·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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