65=10+6t+t^2

Solution for 65=10+6t+t^2 equation:

65=10+6t+t^2

We move all terms to the left:

65-(10+6t+t^2)=0

We get rid of parentheses

-t^2-6t-10+65=0

We add all the numbers together, and all the variables

-1t^2-6t+55=0

a = -1; b = -6; c = +55;
Δ = b2-4ac
Δ = -62-4·(-1)·55
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-16}{2*-1}=\frac{-10}{-2}
=+5
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+16}{2*-1}=\frac{22}{-2}
=-11
$