123+32.56t-4.9t^2=0

Solution for 123+32.56t-4.9t^2=0 equation:

123+32.56t-4.9t^2=0

a = -4.9; b = 32.56; c = +123;
Δ = b2-4ac
Δ = 32.562-4·(-4.9)·123
Δ = 3470.9536
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{-(32.56)-\sqrt{3470.9536}}{2*-4.9}=\frac{-32.56-\sqrt{3470.9536}}{-9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32.56)+\sqrt{3470.9536}}{2*-4.9}=\frac{-32.56+\sqrt{3470.9536}}{-9.8}
$