5t^2+6t-500=0

Solution for 5t^2+6t-500=0 equation:

5t^2+6t-500=0

a = 5; b = 6; c = -500;
Δ = b2-4ac
Δ = 62-4·5·(-500)
Δ = 10036
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:

$\sqrt{\Delta}=\sqrt{10036}=\sqrt{4*2509}=\sqrt{4}*\sqrt{2509}=2\sqrt{2509}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{2509}}{2*5}=\frac{-6-2\sqrt{2509}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{2509}}{2*5}=\frac{-6+2\sqrt{2509}}{10}
$