2.5t+4.9t^2-57=0

Solution for 2.5t+4.9t^2-57=0 equation:

2.5t+4.9t^2-57=0

a = 4.9; b = 2.5; c = -57;
Δ = b2-4ac
Δ = 2.52-4·4.9·(-57)
Δ = 1123.45
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{-(2.5)-\sqrt{1123.45}}{2*4.9}=\frac{-2.5-\sqrt{1123.45}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2.5)+\sqrt{1123.45}}{2*4.9}=\frac{-2.5+\sqrt{1123.45}}{9.8}
$