23=9x2-6x

Solution for 23=9x2-6x equation:

23=9x^2-6x

We move all terms to the left:

23-(9x^2-6x)=0

We get rid of parentheses

-9x^2+6x+23=0

a = -9; b = 6; c = +23;
Δ = b2-4ac
Δ = 62-4·(-9)·23
Δ = 864
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-12\sqrt{6}}{2*-9}=\frac{-6-12\sqrt{6}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+12\sqrt{6}}{2*-9}=\frac{-6+12\sqrt{6}}{-18}
$