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9t^2-1250t+625=0
a = 9; b = -1250; c = +625;
Δ = b2-4ac
Δ = -12502-4·9·625
Δ = 1540000
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}$$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1540000}=\sqrt{10000*154}=\sqrt{10000}*\sqrt{154}=100\sqrt{154}$$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1250)-100\sqrt{154}}{2*9}=\frac{1250-100\sqrt{154}}{18} $$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1250)+100\sqrt{154}}{2*9}=\frac{1250+100\sqrt{154}}{18} $
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