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0=-5t^2+40t+9
We move all terms to the left:
0-(-5t^2+40t+9)=0
We add all the numbers together, and all the variables
-(-5t^2+40t+9)=0
We get rid of parentheses
5t^2-40t-9=0
a = 5; b = -40; c = -9;
Δ = b2-4ac
Δ = -402-4·5·(-9)
Δ = 1780
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}$$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1780}=\sqrt{4*445}=\sqrt{4}*\sqrt{445}=2\sqrt{445}$$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-2\sqrt{445}}{2*5}=\frac{40-2\sqrt{445}}{10} $$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+2\sqrt{445}}{2*5}=\frac{40+2\sqrt{445}}{10} $
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