0=-6+79-6t-5t^2

Solution for 0=-6+79-6t-5t^2 equation:

0=-6+79-6t-5t^2

We move all terms to the left:

0-(-6+79-6t-5t^2)=0

We add all the numbers together, and all the variables

-(-6+79-6t-5t^2)=0

We get rid of parentheses

5t^2+6t+6-79=0

We add all the numbers together, and all the variables

5t^2+6t-73=0

a = 5; b = 6; c = -73;
Δ = b2-4ac
Δ = 62-4·5·(-73)
Δ = 1496
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:

$\sqrt{\Delta}=\sqrt{1496}=\sqrt{4*374}=\sqrt{4}*\sqrt{374}=2\sqrt{374}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{374}}{2*5}=\frac{-6-2\sqrt{374}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{374}}{2*5}=\frac{-6+2\sqrt{374}}{10}
$