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7x^2-8x-17=0
a = 7; b = -8; c = -17;
Δ = b2-4ac
Δ = -82-4·7·(-17)
Δ = 540
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{540}=\sqrt{36*15}=\sqrt{36}*\sqrt{15}=6\sqrt{15}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-6\sqrt{15}}{2*7}=\frac{8-6\sqrt{15}}{14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+6\sqrt{15}}{2*7}=\frac{8+6\sqrt{15}}{14} $
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