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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

16t^2-40t-6=0

a = 16; b = -40; c = -6;
Δ = b2-4ac
Δ = -402-4·16·(-6)
Δ = 1984
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1984}=\sqrt{64*31}=\sqrt{64}*\sqrt{31}=8\sqrt{31}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-8\sqrt{31}}{2*16}=\frac{40-8\sqrt{31}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+8\sqrt{31}}{2*16}=\frac{40+8\sqrt{31}}{32}
$