(x2-4x)2+7(x2-4x)=-12

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Solution for (x2-4x)2+7(x2-4x)=-12 equation:



(x2-4x)2+7(x2-4x)=-12
We move all terms to the left:
(x2-4x)2+7(x2-4x)-(-12)=0
We add all the numbers together, and all the variables
(+x^2-4x)2+7(+x^2-4x)-(-12)=0
We add all the numbers together, and all the variables
(+x^2-4x)2+7(+x^2-4x)+12=0
We multiply parentheses
2x^2+7x^2-8x-28x+12=0
We add all the numbers together, and all the variables
9x^2-36x+12=0
a = 9; b = -36; c = +12;
Δ = b2-4ac
Δ = -362-4·9·12
Δ = 864
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:
$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-12\sqrt{6}}{2*9}=\frac{36-12\sqrt{6}}{18} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+12\sqrt{6}}{2*9}=\frac{36+12\sqrt{6}}{18} $

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