-8-3w(w+13)=4(w+11)-7w

Solution for -8-3w(w+13)=4(w+11)-7w equation:

-8-3w(w+13)=4(w+11)-7w

We move all terms to the left:

-8-3w(w+13)-(4(w+11)-7w)=0

We multiply parentheses

-3w^2-39w-(4(w+11)-7w)-8=0


We calculate terms in parentheses: -(4(w+11)-7w), so:

4(w+11)-7w

We add all the numbers together, and all the variables

-7w+4(w+11)

We multiply parentheses

-7w+4w+44

We add all the numbers together, and all the variables

-3w+44

Back to the equation:

-(-3w+44)


We get rid of parentheses

-3w^2-39w+3w-44-8=0

We add all the numbers together, and all the variables

-3w^2-36w-52=0

a = -3; b = -36; c = -52;
Δ = b2-4ac
Δ = -362-4·(-3)·(-52)
Δ = 672
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{672}=\sqrt{16*42}=\sqrt{16}*\sqrt{42}=4\sqrt{42}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{42}}{2*-3}=\frac{36-4\sqrt{42}}{-6}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{42}}{2*-3}=\frac{36+4\sqrt{42}}{-6}
$