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0=20+20t-12t^2
We move all terms to the left:
0-(20+20t-12t^2)=0
We add all the numbers together, and all the variables
-(20+20t-12t^2)=0
We get rid of parentheses
12t^2-20t-20=0
a = 12; b = -20; c = -20;
Δ = b2-4ac
Δ = -202-4·12·(-20)
Δ = 1360
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}$$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1360}=\sqrt{16*85}=\sqrt{16}*\sqrt{85}=4\sqrt{85}$$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{85}}{2*12}=\frac{20-4\sqrt{85}}{24} $$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{85}}{2*12}=\frac{20+4\sqrt{85}}{24} $
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