96t+16t^2=50

Solution for 96t+16t^2=50 equation:

96t+16t^2=50

We move all terms to the left:

96t+16t^2-(50)=0

a = 16; b = 96; c = -50;
Δ = b2-4ac
Δ = 962-4·16·(-50)
Δ = 12416
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:

$\sqrt{\Delta}=\sqrt{12416}=\sqrt{64*194}=\sqrt{64}*\sqrt{194}=8\sqrt{194}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(96)-8\sqrt{194}}{2*16}=\frac{-96-8\sqrt{194}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(96)+8\sqrt{194}}{2*16}=\frac{-96+8\sqrt{194}}{32}
$