10=3t^2+2t-1

Solution for 10=3t^2+2t-1 equation:

10=3t^2+2t-1

We move all terms to the left:

10-(3t^2+2t-1)=0

We get rid of parentheses

-3t^2-2t+1+10=0

We add all the numbers together, and all the variables

-3t^2-2t+11=0

a = -3; b = -2; c = +11;
Δ = b2-4ac
Δ = -22-4·(-3)·11
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{34}}{2*-3}=\frac{2-2\sqrt{34}}{-6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{34}}{2*-3}=\frac{2+2\sqrt{34}}{-6}
$