T=-4t^2+14t-6

Solution for T=-4t^2+14t-6 equation:

=-4T^2+14T-6

We move all terms to the left:

-(-4T^2+14T-6)=0

We get rid of parentheses

4T^2-14T+6=0

a = 4; b = -14; c = +6;
Δ = b2-4ac
Δ = -142-4·4·6
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$T_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$T_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$T_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-10}{2*4}=\frac{4}{8}
=1/2
$
$T_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+10}{2*4}=\frac{24}{8}
=3
$