24y^2+86y+27=-1

Solution for 24y^2+86y+27=-1 equation:

24y^2+86y+27=-1

We move all terms to the left:

24y^2+86y+27-(-1)=0

We add all the numbers together, and all the variables

24y^2+86y+28=0

a = 24; b = 86; c = +28;
Δ = b2-4ac
Δ = 862-4·24·28
Δ = 4708
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4708}=\sqrt{4*1177}=\sqrt{4}*\sqrt{1177}=2\sqrt{1177}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(86)-2\sqrt{1177}}{2*24}=\frac{-86-2\sqrt{1177}}{48}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(86)+2\sqrt{1177}}{2*24}=\frac{-86+2\sqrt{1177}}{48}
$