4t^2=-12t-5

Solution for 4t^2=-12t-5 equation:

4t^2=-12t-5

We move all terms to the left:

4t^2-(-12t-5)=0

We get rid of parentheses

4t^2+12t+5=0

a = 4; b = 12; c = +5;
Δ = b2-4ac
Δ = 122-4·4·5
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-8}{2*4}=\frac{-20}{8}
=-2+1/2
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+8}{2*4}=\frac{-4}{8}
=-1/2
$