24t=15-6t^2

Solution for 24t=15-6t^2 equation:

24t=15-6t^2

We move all terms to the left:

24t-(15-6t^2)=0

We get rid of parentheses

6t^2+24t-15=0

a = 6; b = 24; c = -15;
Δ = b2-4ac
Δ = 242-4·6·(-15)
Δ = 936
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:

$\sqrt{\Delta}=\sqrt{936}=\sqrt{36*26}=\sqrt{36}*\sqrt{26}=6\sqrt{26}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-6\sqrt{26}}{2*6}=\frac{-24-6\sqrt{26}}{12}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+6\sqrt{26}}{2*6}=\frac{-24+6\sqrt{26}}{12}
$