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(2w+6)w=228
We move all terms to the left:
(2w+6)w-(228)=0
We multiply parentheses
2w^2+6w-228=0
a = 2; b = 6; c = -228;
Δ = b2-4ac
Δ = 62-4·2·(-228)
Δ = 1860
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}$$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1860}=\sqrt{4*465}=\sqrt{4}*\sqrt{465}=2\sqrt{465}$$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{465}}{2*2}=\frac{-6-2\sqrt{465}}{4} $$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{465}}{2*2}=\frac{-6+2\sqrt{465}}{4} $
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