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10x^2-46x+2=0
a = 10; b = -46; c = +2;
Δ = b2-4ac
Δ = -462-4·10·2
Δ = 2036
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2036}=\sqrt{4*509}=\sqrt{4}*\sqrt{509}=2\sqrt{509}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-2\sqrt{509}}{2*10}=\frac{46-2\sqrt{509}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+2\sqrt{509}}{2*10}=\frac{46+2\sqrt{509}}{20} $
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