-4x(5x+4)-x-1=-164

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Solution for -4x(5x+4)-x-1=-164 equation:



-4x(5x+4)-x-1=-164
We move all terms to the left:
-4x(5x+4)-x-1-(-164)=0
We add all the numbers together, and all the variables
-1x-4x(5x+4)+163=0
We multiply parentheses
-20x^2-1x-16x+163=0
We add all the numbers together, and all the variables
-20x^2-17x+163=0
a = -20; b = -17; c = +163;
Δ = b2-4ac
Δ = -172-4·(-20)·163
Δ = 13329
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:
$\sqrt{\Delta}=\sqrt{13329}=\sqrt{9*1481}=\sqrt{9}*\sqrt{1481}=3\sqrt{1481}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-3\sqrt{1481}}{2*-20}=\frac{17-3\sqrt{1481}}{-40} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+3\sqrt{1481}}{2*-20}=\frac{17+3\sqrt{1481}}{-40} $

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