-4.9t^2+5.38t+1.43=2.5

Solution for -4.9t^2+5.38t+1.43=2.5 equation:

-4.9t^2+5.38t+1.43=2.5

We move all terms to the left:

-4.9t^2+5.38t+1.43-(2.5)=0

We add all the numbers together, and all the variables

-4.9t^2+5.38t-1.07=0

a = -4.9; b = 5.38; c = -1.07;
Δ = b2-4ac
Δ = 5.382-4·(-4.9)·(-1.07)
Δ = 7.9724
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{-(5.38)-\sqrt{7.9724}}{2*-4.9}=\frac{-5.38-\sqrt{7.9724}}{-9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5.38)+\sqrt{7.9724}}{2*-4.9}=\frac{-5.38+\sqrt{7.9724}}{-9.8}
$