(8x-4)(17x-23)=(3x+17)

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Solution for (8x-4)(17x-23)=(3x+17) equation:



(8x-4)(17x-23)=(3x+17)
We move all terms to the left:
(8x-4)(17x-23)-((3x+17))=0
We multiply parentheses ..
(+136x^2-184x-68x+92)-((3x+17))=0
We calculate terms in parentheses: -((3x+17)), so:
(3x+17)
We get rid of parentheses
3x+17
Back to the equation:
-(3x+17)
We get rid of parentheses
136x^2-184x-68x-3x+92-17=0
We add all the numbers together, and all the variables
136x^2-255x+75=0
a = 136; b = -255; c = +75;
Δ = b2-4ac
Δ = -2552-4·136·75
Δ = 24225
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:
$\sqrt{\Delta}=\sqrt{24225}=\sqrt{25*969}=\sqrt{25}*\sqrt{969}=5\sqrt{969}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-255)-5\sqrt{969}}{2*136}=\frac{255-5\sqrt{969}}{272} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-255)+5\sqrt{969}}{2*136}=\frac{255+5\sqrt{969}}{272} $

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