0=-5t^2+18t+1

Solution for 0=-5t^2+18t+1 equation:

0=-5t^2+18t+1

We move all terms to the left:

0-(-5t^2+18t+1)=0

We add all the numbers together, and all the variables

-(-5t^2+18t+1)=0

We get rid of parentheses

5t^2-18t-1=0

a = 5; b = -18; c = -1;
Δ = b2-4ac
Δ = -182-4·5·(-1)
Δ = 344
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:

$\sqrt{\Delta}=\sqrt{344}=\sqrt{4*86}=\sqrt{4}*\sqrt{86}=2\sqrt{86}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{86}}{2*5}=\frac{18-2\sqrt{86}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{86}}{2*5}=\frac{18+2\sqrt{86}}{10}
$