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42x^2-219x-252=0
a = 42; b = -219; c = -252;
Δ = b2-4ac
Δ = -2192-4·42·(-252)
Δ = 90297
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{90297}=\sqrt{9*10033}=\sqrt{9}*\sqrt{10033}=3\sqrt{10033}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-219)-3\sqrt{10033}}{2*42}=\frac{219-3\sqrt{10033}}{84} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-219)+3\sqrt{10033}}{2*42}=\frac{219+3\sqrt{10033}}{84} $
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