13x^2=x

Solution for 13x^2=x equation:

13x^2=x

We move all terms to the left:

13x^2-(x)=0

We add all the numbers together, and all the variables

13x^2-1x=0

a = 13; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·13·0
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*13}=\frac{0}{26}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*13}=\frac{2}{26}
=1/13
$