2x+9=-7x(x+2)

Solution for 2x+9=-7x(x+2) equation:

2x+9=-7x(x+2)

We move all terms to the left:

2x+9-(-7x(x+2))=0


We calculate terms in parentheses: -(-7x(x+2)), so:

-7x(x+2)

We multiply parentheses

-7x^2-14x

Back to the equation:

-(-7x^2-14x)


We get rid of parentheses

7x^2+14x+2x+9=0

We add all the numbers together, and all the variables

7x^2+16x+9=0

a = 7; b = 16; c = +9;
Δ = b2-4ac
Δ = 162-4·7·9
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2}{2*7}=\frac{-18}{14}
=-1+2/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2}{2*7}=\frac{-14}{14}
=-1
$