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0=120+-8t+-16t^2
We move all terms to the left:
0-(120+-8t+-16t^2)=0
We add all the numbers together, and all the variables
-(120+-8t+-16t^2)=0
We use the square of the difference formula
-(120-8t-16t^2)=0
We get rid of parentheses
16t^2+8t-120=0
a = 16; b = 8; c = -120;
Δ = b2-4ac
Δ = 82-4·16·(-120)
Δ = 7744
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}$$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{7744}=88$$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-88}{2*16}=\frac{-96}{32} =-3 $$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+88}{2*16}=\frac{80}{32} =2+1/2 $
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