-6t^2-10t+84=0

Solution for -6t^2-10t+84=0 equation:

-6t^2-10t+84=0

a = -6; b = -10; c = +84;
Δ = b2-4ac
Δ = -102-4·(-6)·84
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-46}{2*-6}=\frac{-36}{-12}
=+3
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+46}{2*-6}=\frac{56}{-12}
=-4+2/3
$