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7x^2-35x+14=0
a = 7; b = -35; c = +14;
Δ = b2-4ac
Δ = -352-4·7·14
Δ = 833
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{833}=\sqrt{49*17}=\sqrt{49}*\sqrt{17}=7\sqrt{17}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-7\sqrt{17}}{2*7}=\frac{35-7\sqrt{17}}{14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+7\sqrt{17}}{2*7}=\frac{35+7\sqrt{17}}{14} $
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