6t^2-20t+5=0

Solution for 6t^2-20t+5=0 equation:

6t^2-20t+5=0

a = 6; b = -20; c = +5;
Δ = b2-4ac
Δ = -202-4·6·5
Δ = 280
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:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{70}}{2*6}=\frac{20-2\sqrt{70}}{12}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{70}}{2*6}=\frac{20+2\sqrt{70}}{12}
$