6t^2-34t+43=0

Solution for 6t^2-34t+43=0 equation:

6t^2-34t+43=0

a = 6; b = -34; c = +43;
Δ = b2-4ac
Δ = -342-4·6·43
Δ = 124
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:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{31}}{2*6}=\frac{34-2\sqrt{31}}{12}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{31}}{2*6}=\frac{34+2\sqrt{31}}{12}
$