(9x-4)(-2+5x)-(9x-4)(3x-5)=0

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Solution for (9x-4)(-2+5x)-(9x-4)(3x-5)=0 equation:



(9x-4)(-2+5x)-(9x-4)(3x-5)=0
We add all the numbers together, and all the variables
(9x-4)(5x-2)-(9x-4)(3x-5)=0
We multiply parentheses ..
(+45x^2-18x-20x+8)-(9x-4)(3x-5)=0
We get rid of parentheses
45x^2-18x-20x-(9x-4)(3x-5)+8=0
We multiply parentheses ..
45x^2-(+27x^2-45x-12x+20)-18x-20x+8=0
We add all the numbers together, and all the variables
45x^2-(+27x^2-45x-12x+20)-38x+8=0
We get rid of parentheses
45x^2-27x^2+45x+12x-38x-20+8=0
We add all the numbers together, and all the variables
18x^2+19x-12=0
a = 18; b = 19; c = -12;
Δ = b2-4ac
Δ = 192-4·18·(-12)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-35}{2*18}=\frac{-54}{36} =-1+1/2 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+35}{2*18}=\frac{16}{36} =4/9 $

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