2x(x-4)+1=6x

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Solution for 2x(x-4)+1=6x equation:



2x(x-4)+1=6x
We move all terms to the left:
2x(x-4)+1-(6x)=0
We add all the numbers together, and all the variables
-6x+2x(x-4)+1=0
We multiply parentheses
2x^2-6x-8x+1=0
We add all the numbers together, and all the variables
2x^2-14x+1=0
a = 2; b = -14; c = +1;
Δ = b2-4ac
Δ = -142-4·2·1
Δ = 188
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:
$\sqrt{\Delta}=\sqrt{188}=\sqrt{4*47}=\sqrt{4}*\sqrt{47}=2\sqrt{47}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{47}}{2*2}=\frac{14-2\sqrt{47}}{4} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{47}}{2*2}=\frac{14+2\sqrt{47}}{4} $

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