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x^2/3-343=0
We multiply all the terms by the denominator
x^2-343*3=0
We add all the numbers together, and all the variables
x^2-1029=0
a = 1; b = 0; c = -1029;
Δ = b2-4ac
Δ = 02-4·1·(-1029)
Δ = 4116
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4116}=\sqrt{196*21}=\sqrt{196}*\sqrt{21}=14\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{21}}{2*1}=\frac{0-14\sqrt{21}}{2} =-\frac{14\sqrt{21}}{2} =-7\sqrt{21} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{21}}{2*1}=\frac{0+14\sqrt{21}}{2} =\frac{14\sqrt{21}}{2} =7\sqrt{21} $
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