8x=-4x^2-1

Solution for 8x=-4x^2-1 equation:

8x=-4x^2-1

We move all terms to the left:

8x-(-4x^2-1)=0

We get rid of parentheses

4x^2+8x+1=0

a = 4; b = 8; c = +1;
Δ = b2-4ac
Δ = 82-4·4·1
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{3}}{2*4}=\frac{-8-4\sqrt{3}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{3}}{2*4}=\frac{-8+4\sqrt{3}}{8}
$