(x+3)9x-18=15

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Solution for (x+3)9x-18=15 equation:



(x+3)9x-18=15
We move all terms to the left:
(x+3)9x-18-(15)=0
We add all the numbers together, and all the variables
(x+3)9x-33=0
We multiply parentheses
9x^2+27x-33=0
a = 9; b = 27; c = -33;
Δ = b2-4ac
Δ = 272-4·9·(-33)
Δ = 1917
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:
$\sqrt{\Delta}=\sqrt{1917}=\sqrt{9*213}=\sqrt{9}*\sqrt{213}=3\sqrt{213}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-3\sqrt{213}}{2*9}=\frac{-27-3\sqrt{213}}{18} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+3\sqrt{213}}{2*9}=\frac{-27+3\sqrt{213}}{18} $

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