10t^2-66t+30=0

Solution for 10t^2-66t+30=0 equation:

10t^2-66t+30=0

a = 10; b = -66; c = +30;
Δ = b2-4ac
Δ = -662-4·10·30
Δ = 3156
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:

$\sqrt{\Delta}=\sqrt{3156}=\sqrt{4*789}=\sqrt{4}*\sqrt{789}=2\sqrt{789}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-2\sqrt{789}}{2*10}=\frac{66-2\sqrt{789}}{20}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+2\sqrt{789}}{2*10}=\frac{66+2\sqrt{789}}{20}
$