t=4.9t^2+27t+2.5

Solution for t=4.9t^2+27t+2.5 equation:

t=4.9t^2+27t+2.5

We move all terms to the left:

t-(4.9t^2+27t+2.5)=0

We get rid of parentheses

-4.9t^2+t-27t-2.5=0

We add all the numbers together, and all the variables

-4.9t^2-26t-2.5=0

a = -4.9; b = -26; c = -2.5;
Δ = b2-4ac
Δ = -262-4·(-4.9)·(-2.5)
Δ = 627
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{-(-26)-\sqrt{627}}{2*-4.9}=\frac{26-\sqrt{627}}{-9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+\sqrt{627}}{2*-4.9}=\frac{26+\sqrt{627}}{-9.8}
$