x=7x^2-2x-6

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

x=7x^2-2x-6

We move all terms to the left:

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

We get rid of parentheses

-7x^2+x+2x+6=0

We add all the numbers together, and all the variables

-7x^2+3x+6=0

a = -7; b = 3; c = +6;
Δ = b2-4ac
Δ = 32-4·(-7)·6
Δ = 177
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{177}}{2*-7}=\frac{-3-\sqrt{177}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{177}}{2*-7}=\frac{-3+\sqrt{177}}{-14}
$