2.5=-5t^2+12t+1

Solution for 2.5=-5t^2+12t+1 equation:

2.5=-5t^2+12t+1

We move all terms to the left:

2.5-(-5t^2+12t+1)=0

We get rid of parentheses

5t^2-12t-1+2.5=0

We add all the numbers together, and all the variables

5t^2-12t+1.5=0

a = 5; b = -12; c = +1.5;
Δ = b2-4ac
Δ = -122-4·5·1.5
Δ = 114
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{-(-12)-\sqrt{114}}{2*5}=\frac{12-\sqrt{114}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+\sqrt{114}}{2*5}=\frac{12+\sqrt{114}}{10}
$