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7x^2-29=0
a = 7; b = 0; c = -29;
Δ = b2-4ac
Δ = 02-4·7·(-29)
Δ = 812
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{812}=\sqrt{4*203}=\sqrt{4}*\sqrt{203}=2\sqrt{203}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{203}}{2*7}=\frac{0-2\sqrt{203}}{14} =-\frac{2\sqrt{203}}{14} =-\frac{\sqrt{203}}{7} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{203}}{2*7}=\frac{0+2\sqrt{203}}{14} =\frac{2\sqrt{203}}{14} =\frac{\sqrt{203}}{7} $
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