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5t^2-11t-35=0
a = 5; b = -11; c = -35;
Δ = b2-4ac
Δ = -112-4·5·(-35)
Δ = 821
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}$$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{821}}{2*5}=\frac{11-\sqrt{821}}{10} $$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{821}}{2*5}=\frac{11+\sqrt{821}}{10} $
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