0=6t^2-30t+24

Solution for 0=6t^2-30t+24 equation:

0=6t^2-30t+24

We move all terms to the left:

0-(6t^2-30t+24)=0

We add all the numbers together, and all the variables

-(6t^2-30t+24)=0

We get rid of parentheses

-6t^2+30t-24=0

a = -6; b = 30; c = -24;
Δ = b2-4ac
Δ = 302-4·(-6)·(-24)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-18}{2*-6}=\frac{-48}{-12}
=+4
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+18}{2*-6}=\frac{-12}{-12}
=1
$