10=5*t^2-3*t

Solution for 10=5*t^2-3*t equation:

10=5t^2-3t

We move all terms to the left:

10-(5t^2-3t)=0

We get rid of parentheses

-5t^2+3t+10=0

a = -5; b = 3; c = +10;
Δ = b2-4ac
Δ = 32-4·(-5)·10
Δ = 209
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{-(3)-\sqrt{209}}{2*-5}=\frac{-3-\sqrt{209}}{-10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{209}}{2*-5}=\frac{-3+\sqrt{209}}{-10}
$