-10=6t-t^2

Solution for -10=6t-t^2 equation:

-10=6t-t^2

We move all terms to the left:

-10-(6t-t^2)=0

We get rid of parentheses

t^2-6t-10=0

a = 1; b = -6; c = -10;
Δ = b2-4ac
Δ = -62-4·1·(-10)
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{19}}{2*1}=\frac{6-2\sqrt{19}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{19}}{2*1}=\frac{6+2\sqrt{19}}{2}
$