5=2+15t-5t^2

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

5=2+15t-5t^2

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

5t^2-15t+3=0

a = 5; b = -15; c = +3;
Δ = b2-4ac
Δ = -152-4·5·3
Δ = 165
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{165}}{2*5}=\frac{15-\sqrt{165}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{165}}{2*5}=\frac{15+\sqrt{165}}{10}
$