40=(6+w)w

Solution for 40=(6+w)w equation:

40=(6+w)w

We move all terms to the left:

40-((6+w)w)=0

We add all the numbers together, and all the variables

-((w+6)w)+40=0


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

(w+6)w

We multiply parentheses

w^2+6w

Back to the equation:

-(w^2+6w)


We get rid of parentheses

-w^2-6w+40=0

We add all the numbers together, and all the variables

-1w^2-6w+40=0

a = -1; b = -6; c = +40;
Δ = b2-4ac
Δ = -62-4·(-1)·40
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-14}{2*-1}=\frac{-8}{-2}
=+4
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+14}{2*-1}=\frac{20}{-2}
=-10
$