5t^2-10t-65=0

Solution for 5t^2-10t-65=0 equation:

5t^2-10t-65=0

a = 5; b = -10; c = -65;
Δ = b2-4ac
Δ = -102-4·5·(-65)
Δ = 1400
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:

$\sqrt{\Delta}=\sqrt{1400}=\sqrt{100*14}=\sqrt{100}*\sqrt{14}=10\sqrt{14}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10\sqrt{14}}{2*5}=\frac{10-10\sqrt{14}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10\sqrt{14}}{2*5}=\frac{10+10\sqrt{14}}{10}
$