5x(4x-2)=x

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Solution for 5x(4x-2)=x equation:



5x(4x-2)=x
We move all terms to the left:
5x(4x-2)-(x)=0
We add all the numbers together, and all the variables
-1x+5x(4x-2)=0
We multiply parentheses
20x^2-1x-10x=0
We add all the numbers together, and all the variables
20x^2-11x=0
a = 20; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·20·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-11}{2*20}=\frac{0}{40} =0 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*20}=\frac{22}{40} =11/20 $

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