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2w^2-7w-114=0
a = 2; b = -7; c = -114;
Δ = b2-4ac
Δ = -72-4·2·(-114)
Δ = 961
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{961}=31$$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-31}{2*2}=\frac{-24}{4} =-6 $$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+31}{2*2}=\frac{38}{4} =9+1/2 $
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