(12x^2)-x=13

Solution for (12x^2)-x=13 equation:

(12x^2)-x=13

We move all terms to the left:

(12x^2)-x-(13)=0

We add all the numbers together, and all the variables

12x^2-1x-13=0

a = 12; b = -1; c = -13;
Δ = b2-4ac
Δ = -12-4·12·(-13)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-25}{2*12}=\frac{-24}{24}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+25}{2*12}=\frac{26}{24}
=1+1/12
$