# Solve for t 0=1.4t^2-5t+2.8 0=1.4t2-5t+2.8
Rewrite the equation as 1.4t2-5t+2.8=0.
1.4t2-5t+2.8=0
Factor 0.2 out of 1.4t2-5t+2.8.
Factor 0.2 out of 1.4t2.
0.2(7t2)-5t+2.8=0
Factor 0.2 out of -5t.
0.2(7t2)+0.2(-25t)+2.8=0
Factor 0.2 out of 2.8.
0.2(7t2)+0.2(-25t)+0.2(14)=0
Factor 0.2 out of 0.2(7t2)+0.2(-25t).
0.2(7t2-25t)+0.2(14)=0
Factor 0.2 out of 0.2(7t2-25t)+0.2(14).
0.2(7t2-25t+14)=0
0.2(7t2-25t+14)=0
Divide each term by 0.2 and simplify.
Divide each term in 0.2(7t2-25t+14)=0 by 0.2.
0.2(7t2-25t+14)0.2=00.2
Cancel the common factor of 0.2.
7t2-25t+14=00.2
Divide 0 by 0.2.
7t2-25t+14=0
7t2-25t+14=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=7, b=-25, and c=14 into the quadratic formula and solve for t.
25±(-25)2-4⋅(7⋅14)2⋅7
Simplify.
Simplify the numerator.
Raise -25 to the power of 2.
t=25±625-4⋅(7⋅14)2⋅7
Multiply 7 by 14.
t=25±625-4⋅982⋅7
Multiply -4 by 98.
t=25±625-3922⋅7
Subtract 392 from 625.
t=25±2332⋅7
t=25±2332⋅7
Multiply 2 by 7.
t=25±23314
t=25±23314
The final answer is the combination of both solutions.
t=25+23314,25-23314
The result can be shown in multiple forms.
Exact Form:
t=25+23314,25-23314
Decimal Form:
t=2.87602410…,0.69540446…
Solve for t 0=1.4t^2-5t+2.8

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