9x(x+3)-3=23x-2

Solution for 9x(x+3)-3=23x-2 equation:

9x(x+3)-3=23x-2

We move all terms to the left:

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

We multiply parentheses

9x^2+27x-(23x-2)-3=0

We get rid of parentheses

9x^2+27x-23x+2-3=0

We add all the numbers together, and all the variables

9x^2+4x-1=0

a = 9; b = 4; c = -1;
Δ = b2-4ac
Δ = 42-4·9·(-1)
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{13}}{2*9}=\frac{-4-2\sqrt{13}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{13}}{2*9}=\frac{-4+2\sqrt{13}}{18}
$