7w+6+2w=-12w(w+2)

Solution for 7w+6+2w=-12w(w+2) equation:

7w+6+2w=-12w(w+2)

We move all terms to the left:

7w+6+2w-(-12w(w+2))=0

We add all the numbers together, and all the variables

9w-(-12w(w+2))+6=0


We calculate terms in parentheses: -(-12w(w+2)), so:

-12w(w+2)

We multiply parentheses

-12w^2-24w

Back to the equation:

-(-12w^2-24w)


We get rid of parentheses

12w^2+24w+9w+6=0

We add all the numbers together, and all the variables

12w^2+33w+6=0

a = 12; b = 33; c = +6;
Δ = b2-4ac
Δ = 332-4·12·6
Δ = 801
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:

$\sqrt{\Delta}=\sqrt{801}=\sqrt{9*89}=\sqrt{9}*\sqrt{89}=3\sqrt{89}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-3\sqrt{89}}{2*12}=\frac{-33-3\sqrt{89}}{24}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+3\sqrt{89}}{2*12}=\frac{-33+3\sqrt{89}}{24}
$