x2-10x-2=0

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Solution for x2-10x-2=0 equation:



x2-10x-2=0
We add all the numbers together, and all the variables
x^2-10x-2=0
a = 1; b = -10; c = -2;
Δ = b2-4ac
Δ = -102-4·1·(-2)
Δ = 108
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:
$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-6\sqrt{3}}{2*1}=\frac{10-6\sqrt{3}}{2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+6\sqrt{3}}{2*1}=\frac{10+6\sqrt{3}}{2} $

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