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10x^2-51x-5=0
a = 10; b = -51; c = -5;
Δ = b2-4ac
Δ = -512-4·10·(-5)
Δ = 2801
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-\sqrt{2801}}{2*10}=\frac{51-\sqrt{2801}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+\sqrt{2801}}{2*10}=\frac{51+\sqrt{2801}}{20} $
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