6-3x=18x^2

Solution for 6-3x=18x^2 equation:

6-3x=18x^2

We move all terms to the left:

6-3x-(18x^2)=0

determiningTheFunctionDomain
-18x^2-3x+6=0

a = -18; b = -3; c = +6;
Δ = b2-4ac
Δ = -32-4·(-18)·6
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-21}{2*-18}=\frac{-18}{-36}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+21}{2*-18}=\frac{24}{-36}
=-2/3
$