x^2=-x/12

Solution for x^2=-x/12 equation:

x^2=-x/12

We move all terms to the left:

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

We get rid of parentheses

x^2+x/12=0

We multiply all the terms by the denominator


x^2*12+x=0

Wy multiply elements

12x^2+x=0

a = 12; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·12·0
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*12}=\frac{-2}{24}
=-1/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*12}=\frac{0}{24}
=0
$