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0=-16t^2+100t+6
We move all terms to the left:
0-(-16t^2+100t+6)=0
We add all the numbers together, and all the variables
-(-16t^2+100t+6)=0
We get rid of parentheses
16t^2-100t-6=0
a = 16; b = -100; c = -6;
Δ = b2-4ac
Δ = -1002-4·16·(-6)
Δ = 10384
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}$$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{10384}=\sqrt{16*649}=\sqrt{16}*\sqrt{649}=4\sqrt{649}$$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-4\sqrt{649}}{2*16}=\frac{100-4\sqrt{649}}{32} $$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+4\sqrt{649}}{2*16}=\frac{100+4\sqrt{649}}{32} $
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