3x+1=100x^2

Solution for 3x+1=100x^2 equation:

3x+1=100x^2

We move all terms to the left:

3x+1-(100x^2)=0

determiningTheFunctionDomain
-100x^2+3x+1=0

a = -100; b = 3; c = +1;
Δ = b2-4ac
Δ = 32-4·(-100)·1
Δ = 409
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{409}}{2*-100}=\frac{-3-\sqrt{409}}{-200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{409}}{2*-100}=\frac{-3+\sqrt{409}}{-200}
$