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

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



(x+7)(2x-1)=(2x+1)(2-5)
We move all terms to the left:
(x+7)(2x-1)-((2x+1)(2-5))=0
We add all the numbers together, and all the variables
(x+7)(2x-1)-((2x+1)(-3))=0
We multiply parentheses ..
(+2x^2-1x+14x-7)-((2x+1)(-3))=0
We calculate terms in parentheses: -((2x+1)(-3)), so:
(2x+1)(-3)
We multiply parentheses ..
(-6x-3)
We get rid of parentheses
-6x-3
Back to the equation:
-(-6x-3)
We get rid of parentheses
2x^2-1x+14x+6x-7+3=0
We add all the numbers together, and all the variables
2x^2+19x-4=0
a = 2; b = 19; c = -4;
Δ = b2-4ac
Δ = 192-4·2·(-4)
Δ = 393
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-\sqrt{393}}{2*2}=\frac{-19-\sqrt{393}}{4} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+\sqrt{393}}{2*2}=\frac{-19+\sqrt{393}}{4} $

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