5t^2-2t-32=0

Solution for 5t^2-2t-32=0 equation:

5t^2-2t-32=0

a = 5; b = -2; c = -32;
Δ = b2-4ac
Δ = -22-4·5·(-32)
Δ = 644
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:

$\sqrt{\Delta}=\sqrt{644}=\sqrt{4*161}=\sqrt{4}*\sqrt{161}=2\sqrt{161}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{161}}{2*5}=\frac{2-2\sqrt{161}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{161}}{2*5}=\frac{2+2\sqrt{161}}{10}
$