)=-6t^2+24t+14

Solution for )=-6t^2+24t+14 equation:

)=-6t^2+24t+14

We move all terms to the left:

)-(-6t^2+24t+14)=0

We add all the numbers together, and all the variables

-(-6t^2+24t+14)=0

We get rid of parentheses

6t^2-24t-14=0

a = 6; b = -24; c = -14;
Δ = b2-4ac
Δ = -242-4·6·(-14)
Δ = 912
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:

$\sqrt{\Delta}=\sqrt{912}=\sqrt{16*57}=\sqrt{16}*\sqrt{57}=4\sqrt{57}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{57}}{2*6}=\frac{24-4\sqrt{57}}{12}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{57}}{2*6}=\frac{24+4\sqrt{57}}{12}
$