x^2=4+x(1-6x)

Solution for x^2=4+x(1-6x) equation:

x^2=4+x(1-6x)

We move all terms to the left:

x^2-(4+x(1-6x))=0

We add all the numbers together, and all the variables

x^2-(4+x(-6x+1))=0


We calculate terms in parentheses: -(4+x(-6x+1)), so:

4+x(-6x+1)

determiningTheFunctionDomain
x(-6x+1)+4

We multiply parentheses

-6x^2+x+4

Back to the equation:

-(-6x^2+x+4)


We get rid of parentheses

x^2+6x^2-x-4=0

We add all the numbers together, and all the variables

7x^2-1x-4=0

a = 7; b = -1; c = -4;
Δ = b2-4ac
Δ = -12-4·7·(-4)
Δ = 113
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{-(-1)-\sqrt{113}}{2*7}=\frac{1-\sqrt{113}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{113}}{2*7}=\frac{1+\sqrt{113}}{14}
$