x=83x^2

Solution for x=83x^2 equation:

x=83x^2

We move all terms to the left:

x-(83x^2)=0

determiningTheFunctionDomain
-83x^2+x=0

a = -83; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-83)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-83}=\frac{-2}{-166}
=1/83
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-83}=\frac{0}{-166}
=0
$