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13x^2-65x+26=0
a = 13; b = -65; c = +26;
Δ = b2-4ac
Δ = -652-4·13·26
Δ = 2873
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2873}=\sqrt{169*17}=\sqrt{169}*\sqrt{17}=13\sqrt{17}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-65)-13\sqrt{17}}{2*13}=\frac{65-13\sqrt{17}}{26} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-65)+13\sqrt{17}}{2*13}=\frac{65+13\sqrt{17}}{26} $
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