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0.05t(100+t)=50
We move all terms to the left:
0.05t(100+t)-(50)=0
We add all the numbers together, and all the variables
0.05t(t+100)-50=0
We multiply parentheses
0t^2+0t-50=0
We add all the numbers together, and all the variables
t^2+t-50=0
a = 1; b = 1; c = -50;
Δ = b2-4ac
Δ = 12-4·1·(-50)
Δ = 201
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{-(1)-\sqrt{201}}{2*1}=\frac{-1-\sqrt{201}}{2} $$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{201}}{2*1}=\frac{-1+\sqrt{201}}{2} $
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