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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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


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

w(w+2)

We multiply parentheses

w^2+2w

Back to the equation:

-(w^2+2w)


We get rid of parentheses

-w^2+9w-2w+6=0

We add all the numbers together, and all the variables

-1w^2+7w+6=0

a = -1; b = 7; c = +6;
Δ = b2-4ac
Δ = 72-4·(-1)·6
Δ = 73
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{-(7)-\sqrt{73}}{2*-1}=\frac{-7-\sqrt{73}}{-2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{73}}{2*-1}=\frac{-7+\sqrt{73}}{-2}
$