5t^2-12t-64=0

Solution for 5t^2-12t-64=0 equation:

5t^2-12t-64=0

a = 5; b = -12; c = -64;
Δ = b2-4ac
Δ = -122-4·5·(-64)
Δ = 1424
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:

$\sqrt{\Delta}=\sqrt{1424}=\sqrt{16*89}=\sqrt{16}*\sqrt{89}=4\sqrt{89}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{89}}{2*5}=\frac{12-4\sqrt{89}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{89}}{2*5}=\frac{12+4\sqrt{89}}{10}
$