23=9x^2+4x-3

Solution for 23=9x^2+4x-3 equation:

23=9x^2+4x-3

We move all terms to the left:

23-(9x^2+4x-3)=0

We get rid of parentheses

-9x^2-4x+3+23=0

We add all the numbers together, and all the variables

-9x^2-4x+26=0

a = -9; b = -4; c = +26;
Δ = b2-4ac
Δ = -42-4·(-9)·26
Δ = 952
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:

$\sqrt{\Delta}=\sqrt{952}=\sqrt{4*238}=\sqrt{4}*\sqrt{238}=2\sqrt{238}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{238}}{2*-9}=\frac{4-2\sqrt{238}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{238}}{2*-9}=\frac{4+2\sqrt{238}}{-18}
$