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4w^2+12w+9=121
We move all terms to the left:
4w^2+12w+9-(121)=0
We add all the numbers together, and all the variables
4w^2+12w-112=0
a = 4; b = 12; c = -112;
Δ = b2-4ac
Δ = 122-4·4·(-112)
Δ = 1936
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{1936}=44$$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-44}{2*4}=\frac{-56}{8} =-7 $$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+44}{2*4}=\frac{32}{8} =4 $
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