76=6t+16t^2

Solution for 76=6t+16t^2 equation:

76=6t+16t^2

We move all terms to the left:

76-(6t+16t^2)=0

We get rid of parentheses

-16t^2-6t+76=0

a = -16; b = -6; c = +76;
Δ = b2-4ac
Δ = -62-4·(-16)·76
Δ = 4900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4900}=70$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-70}{2*-16}=\frac{-64}{-32}
=+2
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+70}{2*-16}=\frac{76}{-32}
=-2+3/8
$