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-8t^2+80t+5=0
a = -8; b = 80; c = +5;
Δ = b2-4ac
Δ = 802-4·(-8)·5
Δ = 6560
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6560}=\sqrt{16*410}=\sqrt{16}*\sqrt{410}=4\sqrt{410}$$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-4\sqrt{410}}{2*-8}=\frac{-80-4\sqrt{410}}{-16} $$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+4\sqrt{410}}{2*-8}=\frac{-80+4\sqrt{410}}{-16} $
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