x2-10x+5=0

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Solution for x2-10x+5=0 equation:



x2-10x+5=0
We add all the numbers together, and all the variables
x^2-10x+5=0
a = 1; b = -10; c = +5;
Δ = b2-4ac
Δ = -102-4·1·5
Δ = 80
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:
$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-4\sqrt{5}}{2*1}=\frac{10-4\sqrt{5}}{2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+4\sqrt{5}}{2*1}=\frac{10+4\sqrt{5}}{2} $

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