6-5x=6x^2

Solution for 6-5x=6x^2 equation:

6-5x=6x^2

We move all terms to the left:

6-5x-(6x^2)=0

determiningTheFunctionDomain
-6x^2-5x+6=0

a = -6; b = -5; c = +6;
Δ = b2-4ac
Δ = -52-4·(-6)·6
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-13}{2*-6}=\frac{-8}{-12}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+13}{2*-6}=\frac{18}{-12}
=-1+1/2
$