49=16t^2+56t+32

Solution for 49=16t^2+56t+32 equation:

49=16t^2+56t+32

We move all terms to the left:

49-(16t^2+56t+32)=0

We get rid of parentheses

-16t^2-56t-32+49=0

We add all the numbers together, and all the variables

-16t^2-56t+17=0

a = -16; b = -56; c = +17;
Δ = b2-4ac
Δ = -562-4·(-16)·17
Δ = 4224
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:

$\sqrt{\Delta}=\sqrt{4224}=\sqrt{64*66}=\sqrt{64}*\sqrt{66}=8\sqrt{66}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-8\sqrt{66}}{2*-16}=\frac{56-8\sqrt{66}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+8\sqrt{66}}{2*-16}=\frac{56+8\sqrt{66}}{-32}
$