8=2+15t-5t^2

Solution for 8=2+15t-5t^2 equation:

8=2+15t-5t^2

We move all terms to the left:

8-(2+15t-5t^2)=0

We get rid of parentheses

5t^2-15t-2+8=0

We add all the numbers together, and all the variables

5t^2-15t+6=0

a = 5; b = -15; c = +6;
Δ = b2-4ac
Δ = -152-4·5·6
Δ = 105
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{105}}{2*5}=\frac{15-\sqrt{105}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{105}}{2*5}=\frac{15+\sqrt{105}}{10}
$