50=5t^2+15t

Solution for 50=5t^2+15t equation:

50=5t^2+15t

We move all terms to the left:

50-(5t^2+15t)=0

We get rid of parentheses

-5t^2-15t+50=0

a = -5; b = -15; c = +50;
Δ = b2-4ac
Δ = -152-4·(-5)·50
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-35}{2*-5}=\frac{-20}{-10}
=+2
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+35}{2*-5}=\frac{50}{-10}
=-5
$