-12b^2-40b-24=0

Solution for -12b^2-40b-24=0 equation:

-12b^2-40b-24=0

a = -12; b = -40; c = -24;
Δ = b2-4ac
Δ = -402-4·(-12)·(-24)
Δ = 448
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-8\sqrt{7}}{2*-12}=\frac{40-8\sqrt{7}}{-24}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+8\sqrt{7}}{2*-12}=\frac{40+8\sqrt{7}}{-24}
$