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2a^2-11a-51=0
a = 2; b = -11; c = -51;
Δ = b2-4ac
Δ = -112-4·2·(-51)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{529}=23$$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-23}{2*2}=\frac{-12}{4} =-3 $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+23}{2*2}=\frac{34}{4} =8+1/2 $
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