x2-4x-161=0

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Solution for x2-4x-161=0 equation:



x2-4x-161=0
We add all the numbers together, and all the variables
x^2-4x-161=0
a = 1; b = -4; c = -161;
Δ = b2-4ac
Δ = -42-4·1·(-161)
Δ = 660
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:
$\sqrt{\Delta}=\sqrt{660}=\sqrt{4*165}=\sqrt{4}*\sqrt{165}=2\sqrt{165}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{165}}{2*1}=\frac{4-2\sqrt{165}}{2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{165}}{2*1}=\frac{4+2\sqrt{165}}{2} $

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