0=-3t^2-56t+29

Solution for 0=-3t^2-56t+29 equation:

0=-3t^2-56t+29

We move all terms to the left:

0-(-3t^2-56t+29)=0

We add all the numbers together, and all the variables

-(-3t^2-56t+29)=0

We get rid of parentheses

3t^2+56t-29=0

a = 3; b = 56; c = -29;
Δ = b2-4ac
Δ = 562-4·3·(-29)
Δ = 3484
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:

$\sqrt{\Delta}=\sqrt{3484}=\sqrt{4*871}=\sqrt{4}*\sqrt{871}=2\sqrt{871}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-2\sqrt{871}}{2*3}=\frac{-56-2\sqrt{871}}{6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+2\sqrt{871}}{2*3}=\frac{-56+2\sqrt{871}}{6}
$