x(2x-1)=3x

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



x(2x-1)=3x
We move all terms to the left:
x(2x-1)-(3x)=0
We add all the numbers together, and all the variables
-3x+x(2x-1)=0
We multiply parentheses
2x^2-3x-1x=0
We add all the numbers together, and all the variables
2x^2-4x=0
a = 2; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·2·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*2}=\frac{0}{4} =0 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*2}=\frac{8}{4} =2 $

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