0=1+7t-5t^2-2

Solution for 0=1+7t-5t^2-2 equation:

0=1+7t-5t^2-2

We move all terms to the left:

0-(1+7t-5t^2-2)=0

We add all the numbers together, and all the variables

-(1+7t-5t^2-2)=0

We get rid of parentheses

5t^2-7t-1+2=0

We add all the numbers together, and all the variables

5t^2-7t+1=0

a = 5; b = -7; c = +1;
Δ = b2-4ac
Δ = -72-4·5·1
Δ = 29
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{29}}{2*5}=\frac{7-\sqrt{29}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{29}}{2*5}=\frac{7+\sqrt{29}}{10}
$