40=(w)(w+6)

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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 $

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