5t^2-24t-65=0

Solution for 5t^2-24t-65=0 equation:

5t^2-24t-65=0

a = 5; b = -24; c = -65;
Δ = b2-4ac
Δ = -242-4·5·(-65)
Δ = 1876
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:

$\sqrt{\Delta}=\sqrt{1876}=\sqrt{4*469}=\sqrt{4}*\sqrt{469}=2\sqrt{469}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{469}}{2*5}=\frac{24-2\sqrt{469}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{469}}{2*5}=\frac{24+2\sqrt{469}}{10}
$