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x^2-6x-343=0
a = 1; b = -6; c = -343;
Δ = b2-4ac
Δ = -62-4·1·(-343)
Δ = 1408
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1408}=\sqrt{64*22}=\sqrt{64}*\sqrt{22}=8\sqrt{22}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-8\sqrt{22}}{2*1}=\frac{6-8\sqrt{22}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+8\sqrt{22}}{2*1}=\frac{6+8\sqrt{22}}{2} $
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