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4x^2-17x+14=0
a = 4; b = -17; c = +14;
Δ = b2-4ac
Δ = -172-4·4·14
Δ = 65
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-\sqrt{65}}{2*4}=\frac{17-\sqrt{65}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{65}}{2*4}=\frac{17+\sqrt{65}}{8} $
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