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11x^2-14x=1
We move all terms to the left:
11x^2-14x-(1)=0
a = 11; b = -14; c = -1;
Δ = b2-4ac
Δ = -142-4·11·(-1)
Δ = 240
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-4\sqrt{15}}{2*11}=\frac{14-4\sqrt{15}}{22} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+4\sqrt{15}}{2*11}=\frac{14+4\sqrt{15}}{22} $
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