(9x-)(5x+4)-(9x-1)(3x-1)=0

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Solution for (9x-)(5x+4)-(9x-1)(3x-1)=0 equation:



(9x-)(5x+4)-(9x-1)(3x-1)=0
We add all the numbers together, and all the variables
(+9x)(5x+4)-(9x-1)(3x-1)=0
We multiply parentheses ..
(+45x^2+36x)-(9x-1)(3x-1)=0
We get rid of parentheses
45x^2+36x-(9x-1)(3x-1)=0
We multiply parentheses ..
45x^2-(+27x^2-9x-3x+1)+36x=0
We get rid of parentheses
45x^2-27x^2+9x+3x+36x-1=0
We add all the numbers together, and all the variables
18x^2+48x-1=0
a = 18; b = 48; c = -1;
Δ = b2-4ac
Δ = 482-4·18·(-1)
Δ = 2376
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:
$\sqrt{\Delta}=\sqrt{2376}=\sqrt{36*66}=\sqrt{36}*\sqrt{66}=6\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-6\sqrt{66}}{2*18}=\frac{-48-6\sqrt{66}}{36} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+6\sqrt{66}}{2*18}=\frac{-48+6\sqrt{66}}{36} $

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