85=5t+6t^2

Solution for 85=5t+6t^2 equation:

85=5t+6t^2

We move all terms to the left:

85-(5t+6t^2)=0

We get rid of parentheses

-6t^2-5t+85=0

a = -6; b = -5; c = +85;
Δ = b2-4ac
Δ = -52-4·(-6)·85
Δ = 2065
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{2065}}{2*-6}=\frac{5-\sqrt{2065}}{-12}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{2065}}{2*-6}=\frac{5+\sqrt{2065}}{-12}
$