9x+11=-4x(x+8)

Solution for 9x+11=-4x(x+8) equation:

9x+11=-4x(x+8)

We move all terms to the left:

9x+11-(-4x(x+8))=0


We calculate terms in parentheses: -(-4x(x+8)), so:

-4x(x+8)

We multiply parentheses

-4x^2-32x

Back to the equation:

-(-4x^2-32x)


We get rid of parentheses

4x^2+32x+9x+11=0

We add all the numbers together, and all the variables

4x^2+41x+11=0

a = 4; b = 41; c = +11;
Δ = b2-4ac
Δ = 412-4·4·11
Δ = 1505
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(41)-\sqrt{1505}}{2*4}=\frac{-41-\sqrt{1505}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+\sqrt{1505}}{2*4}=\frac{-41+\sqrt{1505}}{8}
$