(x+3)(5x-1)=(x+3)(2x-7)

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Solution for (x+3)(5x-1)=(x+3)(2x-7) equation:



(x+3)(5x-1)=(x+3)(2x-7)
We move all terms to the left:
(x+3)(5x-1)-((x+3)(2x-7))=0
We multiply parentheses ..
(+5x^2-1x+15x-3)-((x+3)(2x-7))=0
We calculate terms in parentheses: -((x+3)(2x-7)), so:
(x+3)(2x-7)
We multiply parentheses ..
(+2x^2-7x+6x-21)
We get rid of parentheses
2x^2-7x+6x-21
We add all the numbers together, and all the variables
2x^2-1x-21
Back to the equation:
-(2x^2-1x-21)
We get rid of parentheses
5x^2-2x^2-1x+15x+1x-3+21=0
We add all the numbers together, and all the variables
3x^2+15x+18=0
a = 3; b = 15; c = +18;
Δ = b2-4ac
Δ = 152-4·3·18
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3}{2*3}=\frac{-18}{6} =-3 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3}{2*3}=\frac{-12}{6} =-2 $

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