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75t=68.75+15t-5t^2
We move all terms to the left:
75t-(68.75+15t-5t^2)=0
We get rid of parentheses
5t^2-15t+75t-68.75=0
We add all the numbers together, and all the variables
5t^2+60t-68.75=0
a = 5; b = 60; c = -68.75;
Δ = b2-4ac
Δ = 602-4·5·(-68.75)
Δ = 4975
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}$$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4975}=\sqrt{25*199}=\sqrt{25}*\sqrt{199}=5\sqrt{199}$$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-5\sqrt{199}}{2*5}=\frac{-60-5\sqrt{199}}{10} $$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+5\sqrt{199}}{2*5}=\frac{-60+5\sqrt{199}}{10} $
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