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35x^2-142x-48=0
a = 35; b = -142; c = -48;
Δ = b2-4ac
Δ = -1422-4·35·(-48)
Δ = 26884
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{26884}=\sqrt{4*6721}=\sqrt{4}*\sqrt{6721}=2\sqrt{6721}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-142)-2\sqrt{6721}}{2*35}=\frac{142-2\sqrt{6721}}{70} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-142)+2\sqrt{6721}}{2*35}=\frac{142+2\sqrt{6721}}{70} $
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