x(-3)=6x^2

Solution for x(-3)=6x^2 equation:

x(-3)=6x^2

We move all terms to the left:

x(-3)-(6x^2)=0

determiningTheFunctionDomain
-6x^2+x(-3)=0

We multiply parentheses

-6x^2-3x=0

a = -6; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-6)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-6}=\frac{0}{-12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-6}=\frac{6}{-12}
=-1/2
$