6t^2-36t+45=0

Solution for 6t^2-36t+45=0 equation:

6t^2-36t+45=0

a = 6; b = -36; c = +45;
Δ = b2-4ac
Δ = -362-4·6·45
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-6\sqrt{6}}{2*6}=\frac{36-6\sqrt{6}}{12}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+6\sqrt{6}}{2*6}=\frac{36+6\sqrt{6}}{12}
$