35t-5t^2=50

Solution for 35t-5t^2=50 equation:

35t-5t^2=50

We move all terms to the left:

35t-5t^2-(50)=0

a = -5; b = 35; c = -50;
Δ = b2-4ac
Δ = 352-4·(-5)·(-50)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-15}{2*-5}=\frac{-50}{-10}
=+5
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+15}{2*-5}=\frac{-20}{-10}
=+2
$