w+6=2w(w-6)

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

w+6=2w(w-6)

We move all terms to the left:

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


We calculate terms in parentheses: -(2w(w-6)), so:

2w(w-6)

We multiply parentheses

2w^2-12w

Back to the equation:

-(2w^2-12w)


We get rid of parentheses

-2w^2+w+12w+6=0

We add all the numbers together, and all the variables

-2w^2+13w+6=0

a = -2; b = 13; c = +6;
Δ = b2-4ac
Δ = 132-4·(-2)·6
Δ = 217
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-\sqrt{217}}{2*-2}=\frac{-13-\sqrt{217}}{-4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{217}}{2*-2}=\frac{-13+\sqrt{217}}{-4}
$