5t^2-12t-65=0

Solution for 5t^2-12t-65=0 equation:

5t^2-12t-65=0

a = 5; b = -12; c = -65;
Δ = b2-4ac
Δ = -122-4·5·(-65)
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-38}{2*5}=\frac{-26}{10}
=-2+3/5
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+38}{2*5}=\frac{50}{10}
=5
$