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13x^2-4x-91=0
a = 13; b = -4; c = -91;
Δ = b2-4ac
Δ = -42-4·13·(-91)
Δ = 4748
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4748}=\sqrt{4*1187}=\sqrt{4}*\sqrt{1187}=2\sqrt{1187}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{1187}}{2*13}=\frac{4-2\sqrt{1187}}{26} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{1187}}{2*13}=\frac{4+2\sqrt{1187}}{26} $
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