3t=2+8t-t^2

Solution for 3t=2+8t-t^2 equation:

3t=2+8t-t^2

We move all terms to the left:

3t-(2+8t-t^2)=0

We get rid of parentheses

t^2-8t+3t-2=0

We add all the numbers together, and all the variables

t^2-5t-2=0

a = 1; b = -5; c = -2;
Δ = b2-4ac
Δ = -52-4·1·(-2)
Δ = 33
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{-(-5)-\sqrt{33}}{2*1}=\frac{5-\sqrt{33}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{33}}{2*1}=\frac{5+\sqrt{33}}{2}
$