8-2x=100x^2

Solution for 8-2x=100x^2 equation:

8-2x=100x^2

We move all terms to the left:

8-2x-(100x^2)=0

determiningTheFunctionDomain
-100x^2-2x+8=0

a = -100; b = -2; c = +8;
Δ = b2-4ac
Δ = -22-4·(-100)·8
Δ = 3204
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:

$\sqrt{\Delta}=\sqrt{3204}=\sqrt{36*89}=\sqrt{36}*\sqrt{89}=6\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-6\sqrt{89}}{2*-100}=\frac{2-6\sqrt{89}}{-200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+6\sqrt{89}}{2*-100}=\frac{2+6\sqrt{89}}{-200}
$