# Solve for t s=7t^2+t+5

s=7t2+t+5
Rewrite the equation as 7t2+t+5=s.
7t2+t+5=s
Move s to the left side of the equation by subtracting it from both sides.
7t2+t+5-s=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=7, b=1, and c=5-s into the quadratic formula and solve for t.
-1±12-4⋅(7⋅(5-s))2⋅7
Simplify.
Simplify the numerator.
One to any power is one.
t=-1±1-4⋅(7⋅(5-s))2⋅7
Apply the distributive property.
t=-1±1-4⋅(7⋅5+7(-s))2⋅7
Multiply 7 by 5.
t=-1±1-4⋅(35+7(-s))2⋅7
Multiply -1 by 7.
t=-1±1-4⋅(35-7s)2⋅7
Apply the distributive property.
t=-1±1-4⋅35-4(-7s)2⋅7
Multiply -4 by 35.
t=-1±1-140-4(-7s)2⋅7
Multiply -7 by -4.
t=-1±1-140+28s2⋅7
Subtract 140 from 1.
t=-1±-139+28s2⋅7
t=-1±-139+28s2⋅7
Multiply 2 by 7.
t=-1±-139+28s14
t=-1±-139+28s14
The final answer is the combination of both solutions.
t=-1–139+28s14
t=-1+28s-13914
Solve for t s=7t^2+t+5

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