12=-8w(w+6)

Solution for 12=-8w(w+6) equation:

12=-8w(w+6)

We move all terms to the left:

12-(-8w(w+6))=0


We calculate terms in parentheses: -(-8w(w+6)), so:

-8w(w+6)

We multiply parentheses

-8w^2-48w

Back to the equation:

-(-8w^2-48w)


We get rid of parentheses

8w^2+48w+12=0

a = 8; b = 48; c = +12;
Δ = b2-4ac
Δ = 482-4·8·12
Δ = 1920
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:

$\sqrt{\Delta}=\sqrt{1920}=\sqrt{64*30}=\sqrt{64}*\sqrt{30}=8\sqrt{30}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-8\sqrt{30}}{2*8}=\frac{-48-8\sqrt{30}}{16}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+8\sqrt{30}}{2*8}=\frac{-48+8\sqrt{30}}{16}
$