6=-16t^2+46t+6

Solution for 6=-16t^2+46t+6 equation:

6=-16t^2+46t+6

We move all terms to the left:

6-(-16t^2+46t+6)=0

We get rid of parentheses

16t^2-46t-6+6=0

We add all the numbers together, and all the variables

16t^2-46t=0

a = 16; b = -46; c = 0;
Δ = b2-4ac
Δ = -462-4·16·0
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-46}{2*16}=\frac{0}{32}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+46}{2*16}=\frac{92}{32}
=2+7/8
$