3=16t^2-194t+10

Solution for 3=16t^2-194t+10 equation:

3=16t^2-194t+10

We move all terms to the left:

3-(16t^2-194t+10)=0

We get rid of parentheses

-16t^2+194t-10+3=0

We add all the numbers together, and all the variables

-16t^2+194t-7=0

a = -16; b = 194; c = -7;
Δ = b2-4ac
Δ = 1942-4·(-16)·(-7)
Δ = 37188
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:

$\sqrt{\Delta}=\sqrt{37188}=\sqrt{36*1033}=\sqrt{36}*\sqrt{1033}=6\sqrt{1033}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(194)-6\sqrt{1033}}{2*-16}=\frac{-194-6\sqrt{1033}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(194)+6\sqrt{1033}}{2*-16}=\frac{-194+6\sqrt{1033}}{-32}
$