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

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



3x(x-2)-4=2(x-1)-2
We move all terms to the left:
3x(x-2)-4-(2(x-1)-2)=0
We multiply parentheses
3x^2-6x-(2(x-1)-2)-4=0
We calculate terms in parentheses: -(2(x-1)-2), so:
2(x-1)-2
We multiply parentheses
2x-2-2
We add all the numbers together, and all the variables
2x-4
Back to the equation:
-(2x-4)
We get rid of parentheses
3x^2-6x-2x+4-4=0
We add all the numbers together, and all the variables
3x^2-8x=0
a = 3; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·3·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*3}=\frac{0}{6} =0 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*3}=\frac{16}{6} =2+2/3 $

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