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52x^2-121=0
a = 52; b = 0; c = -121;
Δ = b2-4ac
Δ = 02-4·52·(-121)
Δ = 25168
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{25168}=\sqrt{1936*13}=\sqrt{1936}*\sqrt{13}=44\sqrt{13}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-44\sqrt{13}}{2*52}=\frac{0-44\sqrt{13}}{104} =-\frac{44\sqrt{13}}{104} =-\frac{11\sqrt{13}}{26} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+44\sqrt{13}}{2*52}=\frac{0+44\sqrt{13}}{104} =\frac{44\sqrt{13}}{104} =\frac{11\sqrt{13}}{26} $
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