40=(w)(w+6)

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

40=(w)(w+6)

We move all terms to the left:

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


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

w(w+6)

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
$