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x^2-8x-2020=0
a = 1; b = -8; c = -2020;
Δ = b2-4ac
Δ = -82-4·1·(-2020)
Δ = 8144
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{8144}=\sqrt{16*509}=\sqrt{16}*\sqrt{509}=4\sqrt{509}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{509}}{2*1}=\frac{8-4\sqrt{509}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{509}}{2*1}=\frac{8+4\sqrt{509}}{2} $
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