6t^2-30t+25=0

Solution for 6t^2-30t+25=0 equation:

6t^2-30t+25=0

a = 6; b = -30; c = +25;
Δ = b2-4ac
Δ = -302-4·6·25
Δ = 300
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:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-10\sqrt{3}}{2*6}=\frac{30-10\sqrt{3}}{12}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+10\sqrt{3}}{2*6}=\frac{30+10\sqrt{3}}{12}
$