(9x+15)*(3x-15)=x

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



(9x+15)(3x-15)=x
We move all terms to the left:
(9x+15)(3x-15)-(x)=0
We add all the numbers together, and all the variables
-1x+(9x+15)(3x-15)=0
We multiply parentheses ..
(+27x^2-135x+45x-225)-1x=0
We get rid of parentheses
27x^2-135x+45x-1x-225=0
We add all the numbers together, and all the variables
27x^2-91x-225=0
a = 27; b = -91; c = -225;
Δ = b2-4ac
Δ = -912-4·27·(-225)
Δ = 32581
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-91)-\sqrt{32581}}{2*27}=\frac{91-\sqrt{32581}}{54} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-91)+\sqrt{32581}}{2*27}=\frac{91+\sqrt{32581}}{54} $

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