x^2-22x-4=0

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Solution for x^2-22x-4=0 equation:



x^2-22x-4=0
a = 1; b = -22; c = -4;
Δ = b2-4ac
Δ = -222-4·1·(-4)
Δ = 500
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:
$\sqrt{\Delta}=\sqrt{500}=\sqrt{100*5}=\sqrt{100}*\sqrt{5}=10\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-10\sqrt{5}}{2*1}=\frac{22-10\sqrt{5}}{2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+10\sqrt{5}}{2*1}=\frac{22+10\sqrt{5}}{2} $

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