-4x(x+1)+2x=3(2x-1)

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Solution for -4x(x+1)+2x=3(2x-1) equation:



-4x(x+1)+2x=3(2x-1)
We move all terms to the left:
-4x(x+1)+2x-(3(2x-1))=0
We add all the numbers together, and all the variables
2x-4x(x+1)-(3(2x-1))=0
We multiply parentheses
-4x^2+2x-4x-(3(2x-1))=0
We calculate terms in parentheses: -(3(2x-1)), so:
3(2x-1)
We multiply parentheses
6x-3
Back to the equation:
-(6x-3)
We add all the numbers together, and all the variables
-4x^2-2x-(6x-3)=0
We get rid of parentheses
-4x^2-2x-6x+3=0
We add all the numbers together, and all the variables
-4x^2-8x+3=0
a = -4; b = -8; c = +3;
Δ = b2-4ac
Δ = -82-4·(-4)·3
Δ = 112
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:
$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{7}}{2*-4}=\frac{8-4\sqrt{7}}{-8} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{7}}{2*-4}=\frac{8+4\sqrt{7}}{-8} $

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