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

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

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

We move all terms to the left:

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

We get rid of parentheses

4t^2+4t+24t+24=0

We add all the numbers together, and all the variables

4t^2+28t+24=0

a = 4; b = 28; c = +24;
Δ = b2-4ac
Δ = 282-4·4·24
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-20}{2*4}=\frac{-48}{8}
=-6
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+20}{2*4}=\frac{-8}{8}
=-1
$