5t^2-15t-200=0

Solution for 5t^2-15t-200=0 equation:

5t^2-15t-200=0

a = 5; b = -15; c = -200;
Δ = b2-4ac
Δ = -152-4·5·(-200)
Δ = 4225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4225}=65$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-65}{2*5}=\frac{-50}{10}
=-5
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+65}{2*5}=\frac{80}{10}
=8
$