5=1+15t-5t^2

Solution for 5=1+15t-5t^2 equation:

5=1+15t-5t^2

We move all terms to the left:

5-(1+15t-5t^2)=0

We get rid of parentheses

5t^2-15t-1+5=0

We add all the numbers together, and all the variables

5t^2-15t+4=0

a = 5; b = -15; c = +4;
Δ = b2-4ac
Δ = -152-4·5·4
Δ = 145
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{-(-15)-\sqrt{145}}{2*5}=\frac{15-\sqrt{145}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{145}}{2*5}=\frac{15+\sqrt{145}}{10}
$