8-6x=9x^2

Solution for 8-6x=9x^2 equation:

8-6x=9x^2

We move all terms to the left:

8-6x-(9x^2)=0

determiningTheFunctionDomain
-9x^2-6x+8=0

a = -9; b = -6; c = +8;
Δ = b2-4ac
Δ = -62-4·(-9)·8
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-18}{2*-9}=\frac{-12}{-18}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+18}{2*-9}=\frac{24}{-18}
=-1+1/3
$