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16x^2-34x+5=0
a = 16; b = -34; c = +5;
Δ = b2-4ac
Δ = -342-4·16·5
Δ = 836
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{836}=\sqrt{4*209}=\sqrt{4}*\sqrt{209}=2\sqrt{209}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{209}}{2*16}=\frac{34-2\sqrt{209}}{32} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{209}}{2*16}=\frac{34+2\sqrt{209}}{32} $
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