w(18+8w)=35

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Solution for w(18+8w)=35 equation:



w(18+8w)=35
We move all terms to the left:
w(18+8w)-(35)=0
We add all the numbers together, and all the variables
w(8w+18)-35=0
We multiply parentheses
8w^2+18w-35=0
a = 8; b = 18; c = -35;
Δ = b2-4ac
Δ = 182-4·8·(-35)
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-38}{2*8}=\frac{-56}{16} =-3+1/2 $
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+38}{2*8}=\frac{20}{16} =1+1/4 $

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