8x2+32x-4=-2

Solution for 8x2+32x-4=-2 equation:

8x^2+32x-4=-2

We move all terms to the left:

8x^2+32x-4-(-2)=0

We add all the numbers together, and all the variables

8x^2+32x-2=0

a = 8; b = 32; c = -2;
Δ = b2-4ac
Δ = 322-4·8·(-2)
Δ = 1088
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1088}=\sqrt{64*17}=\sqrt{64}*\sqrt{17}=8\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-8\sqrt{17}}{2*8}=\frac{-32-8\sqrt{17}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+8\sqrt{17}}{2*8}=\frac{-32+8\sqrt{17}}{16}
$