-16t^2+36t+13=19.42

Solution for -16t^2+36t+13=19.42 equation:

-16t^2+36t+13=19.42

We move all terms to the left:

-16t^2+36t+13-(19.42)=0

We add all the numbers together, and all the variables

-16t^2+36t-6.42=0

a = -16; b = 36; c = -6.42;
Δ = b2-4ac
Δ = 362-4·(-16)·(-6.42)
Δ = 885.12
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{-(36)-\sqrt{885.12}}{2*-16}=\frac{-36-\sqrt{885.12}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+\sqrt{885.12}}{2*-16}=\frac{-36+\sqrt{885.12}}{-32}
$