-1/6-7x=x^2

Solution for -1/6-7x=x^2 equation:

-1/6-7x=x^2

We move all terms to the left:

-1/6-7x-(x^2)=0

determiningTheFunctionDomain
-x^2-7x-1/6=0

We add all the numbers together, and all the variables

-1x^2-7x-1/6=0

We multiply all the terms by the denominator


-1x^2*6-7x*6-1=0

Wy multiply elements

-6x^2-42x-1=0

a = -6; b = -42; c = -1;
Δ = b2-4ac
Δ = -422-4·(-6)·(-1)
Δ = 1740
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:

$\sqrt{\Delta}=\sqrt{1740}=\sqrt{4*435}=\sqrt{4}*\sqrt{435}=2\sqrt{435}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{435}}{2*-6}=\frac{42-2\sqrt{435}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{435}}{2*-6}=\frac{42+2\sqrt{435}}{-12}
$