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-5t^2+65t+25=0
a = -5; b = 65; c = +25;
Δ = b2-4ac
Δ = 652-4·(-5)·25
Δ = 4725
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}$$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4725}=\sqrt{225*21}=\sqrt{225}*\sqrt{21}=15\sqrt{21}$$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(65)-15\sqrt{21}}{2*-5}=\frac{-65-15\sqrt{21}}{-10} $$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(65)+15\sqrt{21}}{2*-5}=\frac{-65+15\sqrt{21}}{-10} $
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