4x(x+8)=-13-2x

Solution for 4x(x+8)=-13-2x equation:

4x(x+8)=-13-2x

We move all terms to the left:

4x(x+8)-(-13-2x)=0

We add all the numbers together, and all the variables

4x(x+8)-(-2x-13)=0

We multiply parentheses

4x^2+32x-(-2x-13)=0

We get rid of parentheses

4x^2+32x+2x+13=0

We add all the numbers together, and all the variables

4x^2+34x+13=0

a = 4; b = 34; c = +13;
Δ = b2-4ac
Δ = 342-4·4·13
Δ = 948
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{948}=\sqrt{4*237}=\sqrt{4}*\sqrt{237}=2\sqrt{237}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2\sqrt{237}}{2*4}=\frac{-34-2\sqrt{237}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2\sqrt{237}}{2*4}=\frac{-34+2\sqrt{237}}{8}
$