125=-16t^2+85t+(1/12)

Solution for 125=-16t^2+85t+(1/12) equation:

125=-16t^2+85t+(1/12)

We move all terms to the left:

125-(-16t^2+85t+(1/12))=0

We add all the numbers together, and all the variables

-(-16t^2+85t+(+1/12))+125=0

We multiply all the terms by the denominator


-(-16t^2+85t+(+1+125*12))=0


We calculate terms in parentheses: -(-16t^2+85t+(+1+125*12)), so:

-16t^2+85t+(+1+125*12)

We add all the numbers together, and all the variables

-16t^2+85t+1501

Back to the equation:

-(-16t^2+85t+1501)


We get rid of parentheses

16t^2-85t-1501=0

a = 16; b = -85; c = -1501;
Δ = b2-4ac
Δ = -852-4·16·(-1501)
Δ = 103289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-85)-\sqrt{103289}}{2*16}=\frac{85-\sqrt{103289}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-85)+\sqrt{103289}}{2*16}=\frac{85+\sqrt{103289}}{32}
$