78=7t+16t^2

Solution for 78=7t+16t^2 equation:

78=7t+16t^2

We move all terms to the left:

78-(7t+16t^2)=0

We get rid of parentheses

-16t^2-7t+78=0

a = -16; b = -7; c = +78;
Δ = b2-4ac
Δ = -72-4·(-16)·78
Δ = 5041
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5041}=71$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-71}{2*-16}=\frac{-64}{-32}
=+2
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+71}{2*-16}=\frac{78}{-32}
=-2+7/16
$