-8+24t=40-4t^2

Solution for -8+24t=40-4t^2 equation:

-8+24t=40-4t^2

We move all terms to the left:

-8+24t-(40-4t^2)=0

We get rid of parentheses

4t^2+24t-40-8=0

We add all the numbers together, and all the variables

4t^2+24t-48=0

a = 4; b = 24; c = -48;
Δ = b2-4ac
Δ = 242-4·4·(-48)
Δ = 1344
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:

$\sqrt{\Delta}=\sqrt{1344}=\sqrt{64*21}=\sqrt{64}*\sqrt{21}=8\sqrt{21}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-8\sqrt{21}}{2*4}=\frac{-24-8\sqrt{21}}{8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+8\sqrt{21}}{2*4}=\frac{-24+8\sqrt{21}}{8}
$