(2x-1)(5x-7)=(2x-1)(9-7x)

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Solution for (2x-1)(5x-7)=(2x-1)(9-7x) equation:



(2x-1)(5x-7)=(2x-1)(9-7x)
We move all terms to the left:
(2x-1)(5x-7)-((2x-1)(9-7x))=0
We add all the numbers together, and all the variables
(2x-1)(5x-7)-((2x-1)(-7x+9))=0
We multiply parentheses ..
(+10x^2-14x-5x+7)-((2x-1)(-7x+9))=0
We calculate terms in parentheses: -((2x-1)(-7x+9)), so:
(2x-1)(-7x+9)
We multiply parentheses ..
(-14x^2+18x+7x-9)
We get rid of parentheses
-14x^2+18x+7x-9
We add all the numbers together, and all the variables
-14x^2+25x-9
Back to the equation:
-(-14x^2+25x-9)
We get rid of parentheses
10x^2+14x^2-14x-5x-25x+7+9=0
We add all the numbers together, and all the variables
24x^2-44x+16=0
a = 24; b = -44; c = +16;
Δ = b2-4ac
Δ = -442-4·24·16
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-20}{2*24}=\frac{24}{48} =1/2 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+20}{2*24}=\frac{64}{48} =1+1/3 $

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