6.5t^2+65t+71.5=0

Solution for 6.5t^2+65t+71.5=0 equation:

6.5t^2+65t+71.5=0

a = 6.5; b = 65; c = +71.5;
Δ = b2-4ac
Δ = 652-4·6.5·71.5
Δ = 2366
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:

$\sqrt{\Delta}=\sqrt{2366}=\sqrt{169*14}=\sqrt{169}*\sqrt{14}=13\sqrt{14}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(65)-13\sqrt{14}}{2*6.5}=\frac{-65-13\sqrt{14}}{13}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(65)+13\sqrt{14}}{2*6.5}=\frac{-65+13\sqrt{14}}{13}
$