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5t^2-12t-32=0
a = 5; b = -12; c = -32;
Δ = b2-4ac
Δ = -122-4·5·(-32)
Δ = 784
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}$$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{784}=28$$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-28}{2*5}=\frac{-16}{10} =-1+3/5 $$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+28}{2*5}=\frac{40}{10} =4 $
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