x=-6x^2+1

Solution for x=-6x^2+1 equation:

x=-6x^2+1

We move all terms to the left:

x-(-6x^2+1)=0

We get rid of parentheses

6x^2+x-1=0

a = 6; b = 1; c = -1;
Δ = b2-4ac
Δ = 12-4·6·(-1)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-5}{2*6}=\frac{-6}{12}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+5}{2*6}=\frac{4}{12}
=1/3
$