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

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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} $

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