5x-17=3x(x-3)+2x(x-4)

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Solution for 5x-17=3x(x-3)+2x(x-4) equation:



5x-17=3x(x-3)+2x(x-4)
We move all terms to the left:
5x-17-(3x(x-3)+2x(x-4))=0
We calculate terms in parentheses: -(3x(x-3)+2x(x-4)), so:
3x(x-3)+2x(x-4)
We multiply parentheses
3x^2+2x^2-9x-8x
We add all the numbers together, and all the variables
5x^2-17x
Back to the equation:
-(5x^2-17x)
We get rid of parentheses
-5x^2+5x+17x-17=0
We add all the numbers together, and all the variables
-5x^2+22x-17=0
a = -5; b = 22; c = -17;
Δ = b2-4ac
Δ = 222-4·(-5)·(-17)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-12}{2*-5}=\frac{-34}{-10} =3+2/5 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+12}{2*-5}=\frac{-10}{-10} =1 $

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