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13x^2-7=0
a = 13; b = 0; c = -7;
Δ = b2-4ac
Δ = 02-4·13·(-7)
Δ = 364
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{364}=\sqrt{4*91}=\sqrt{4}*\sqrt{91}=2\sqrt{91}x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{91}}{2*13}=\frac{0-2\sqrt{91}}{26} =-\frac{2\sqrt{91}}{26} =-\frac{\sqrt{91}}{13}x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{91}}{2*13}=\frac{0+2\sqrt{91}}{26} =\frac{2\sqrt{91}}{26} =\frac{\sqrt{91}}{13}
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