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135=-16t^2+169+100
We move all terms to the left:
135-(-16t^2+169+100)=0
We get rid of parentheses
16t^2-169-100+135=0
We add all the numbers together, and all the variables
16t^2-134=0
a = 16; b = 0; c = -134;
Δ = b2-4ac
Δ = 02-4·16·(-134)
Δ = 8576
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}$$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{8576}=\sqrt{64*134}=\sqrt{64}*\sqrt{134}=8\sqrt{134}$$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{134}}{2*16}=\frac{0-8\sqrt{134}}{32} =-\frac{8\sqrt{134}}{32} =-\frac{\sqrt{134}}{4} $$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{134}}{2*16}=\frac{0+8\sqrt{134}}{32} =\frac{8\sqrt{134}}{32} =\frac{\sqrt{134}}{4} $
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