3t^2-16t+3=0

Solution for 3t^2-16t+3=0 equation:

3t^2-16t+3=0

a = 3; b = -16; c = +3;
Δ = b2-4ac
Δ = -162-4·3·3
Δ = 220
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:

$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{55}}{2*3}=\frac{16-2\sqrt{55}}{6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{55}}{2*3}=\frac{16+2\sqrt{55}}{6}
$