-7x2=x

Solution for -7x2=x equation:

-7x^2=x

We move all terms to the left:

-7x^2-(x)=0

We add all the numbers together, and all the variables

-7x^2-1x=0

a = -7; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-7)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-7}=\frac{0}{-14}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-7}=\frac{2}{-14}
=-1/7
$