50+30t=2t^2

Solution for 50+30t=2t^2 equation:

50+30t=2t^2

We move all terms to the left:

50+30t-(2t^2)=0

determiningTheFunctionDomain
-2t^2+30t+50=0

a = -2; b = 30; c = +50;
Δ = b2-4ac
Δ = 302-4·(-2)·50
Δ = 1300
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:

$\sqrt{\Delta}=\sqrt{1300}=\sqrt{100*13}=\sqrt{100}*\sqrt{13}=10\sqrt{13}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-10\sqrt{13}}{2*-2}=\frac{-30-10\sqrt{13}}{-4}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+10\sqrt{13}}{2*-2}=\frac{-30+10\sqrt{13}}{-4}
$