24t=21+6t2

Solution for 24t=21+6t2 equation:

24t=21+6t^2

We move all terms to the left:

24t-(21+6t^2)=0

We get rid of parentheses

-6t^2+24t-21=0

a = -6; b = 24; c = -21;
Δ = b2-4ac
Δ = 242-4·(-6)·(-21)
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-6\sqrt{2}}{2*-6}=\frac{-24-6\sqrt{2}}{-12}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+6\sqrt{2}}{2*-6}=\frac{-24+6\sqrt{2}}{-12}
$