-6t^2+43t-77=0

Solution for -6t^2+43t-77=0 equation:

-6t^2+43t-77=0

a = -6; b = 43; c = -77;
Δ = b2-4ac
Δ = 432-4·(-6)·(-77)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(43)-1}{2*-6}=\frac{-44}{-12}
=3+2/3
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(43)+1}{2*-6}=\frac{-42}{-12}
=3+1/2
$