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12x^2-42x+5=0
a = 12; b = -42; c = +5;
Δ = b2-4ac
Δ = -422-4·12·5
Δ = 1524
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1524}=\sqrt{4*381}=\sqrt{4}*\sqrt{381}=2\sqrt{381}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{381}}{2*12}=\frac{42-2\sqrt{381}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{381}}{2*12}=\frac{42+2\sqrt{381}}{24} $
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