2x=-3x(x+5)

Solution for 2x=-3x(x+5) equation:

2x=-3x(x+5)

We move all terms to the left:

2x-(-3x(x+5))=0


We calculate terms in parentheses: -(-3x(x+5)), so:

-3x(x+5)

We multiply parentheses

-3x^2-15x

Back to the equation:

-(-3x^2-15x)


We get rid of parentheses

3x^2+15x+2x=0

We add all the numbers together, and all the variables

3x^2+17x=0

a = 3; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·3·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*3}=\frac{-34}{6}
=-5+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*3}=\frac{0}{6}
=0
$