0=x^2+16x-4

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Solution for 0=x^2+16x-4 equation:



0=x^2+16x-4
We move all terms to the left:
0-(x^2+16x-4)=0
We add all the numbers together, and all the variables
-(x^2+16x-4)=0
We get rid of parentheses
-x^2-16x+4=0
We add all the numbers together, and all the variables
-1x^2-16x+4=0
a = -1; b = -16; c = +4;
Δ = b2-4ac
Δ = -162-4·(-1)·4
Δ = 272
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:
$\sqrt{\Delta}=\sqrt{272}=\sqrt{16*17}=\sqrt{16}*\sqrt{17}=4\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{17}}{2*-1}=\frac{16-4\sqrt{17}}{-2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{17}}{2*-1}=\frac{16+4\sqrt{17}}{-2} $

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