t=-t2+10t+75

Solution for t=-t2+10t+75 equation:

t=-t2+10t+75

We move all terms to the left:

t-(-t2+10t+75)=0

We add all the numbers together, and all the variables

-(-1t^2+10t+75)+t=0

We get rid of parentheses

1t^2-10t+t-75=0

We add all the numbers together, and all the variables

t^2-9t-75=0

a = 1; b = -9; c = -75;
Δ = b2-4ac
Δ = -92-4·1·(-75)
Δ = 381
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{-(-9)-\sqrt{381}}{2*1}=\frac{9-\sqrt{381}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{381}}{2*1}=\frac{9+\sqrt{381}}{2}
$