6t^2-30t+29=0

Solution for 6t^2-30t+29=0 equation:

6t^2-30t+29=0

a = 6; b = -30; c = +29;
Δ = b2-4ac
Δ = -302-4·6·29
Δ = 204
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:

$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{51}}{2*6}=\frac{30-2\sqrt{51}}{12}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{51}}{2*6}=\frac{30+2\sqrt{51}}{12}
$