78.4=4.9*t^2

Solution for 78.4=4.9*t^2 equation:

78.4=4.9t^2

We move all terms to the left:

78.4-(4.9t^2)=0

We get rid of parentheses

-4.9t^2+78.4=0

a = -4.9; b = 0; c = +78.4;
Δ = b2-4ac
Δ = 02-4·(-4.9)·78.4
Δ = 1536.64
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{-(0)-\sqrt{1536.64}}{2*-4.9}=\frac{0-\sqrt{1536.64}}{-9.8}
=-\frac{\sqrt{}}{-9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+\sqrt{1536.64}}{2*-4.9}=\frac{0+\sqrt{1536.64}}{-9.8}
=\frac{\sqrt{}}{-9.8}
$