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20x^2-8x-71=0
a = 20; b = -8; c = -71;
Δ = b2-4ac
Δ = -82-4·20·(-71)
Δ = 5744
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{5744}=\sqrt{16*359}=\sqrt{16}*\sqrt{359}=4\sqrt{359}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{359}}{2*20}=\frac{8-4\sqrt{359}}{40} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{359}}{2*20}=\frac{8+4\sqrt{359}}{40} $
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