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589x^2-17670x+589=0
a = 589; b = -17670; c = +589;
Δ = b2-4ac
Δ = -176702-4·589·589
Δ = 310841216
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{310841216}=\sqrt{22202944*14}=\sqrt{22202944}*\sqrt{14}=4712\sqrt{14}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17670)-4712\sqrt{14}}{2*589}=\frac{17670-4712\sqrt{14}}{1178} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17670)+4712\sqrt{14}}{2*589}=\frac{17670+4712\sqrt{14}}{1178} $
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