3t^2-10t-6=14

Solution for 3t^2-10t-6=14 equation:

3t^2-10t-6=14

We move all terms to the left:

3t^2-10t-6-(14)=0

We add all the numbers together, and all the variables

3t^2-10t-20=0

a = 3; b = -10; c = -20;
Δ = b2-4ac
Δ = -102-4·3·(-20)
Δ = 340
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:

$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{85}}{2*3}=\frac{10-2\sqrt{85}}{6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{85}}{2*3}=\frac{10+2\sqrt{85}}{6}
$