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7x^2-122x-2352=0
a = 7; b = -122; c = -2352;
Δ = b2-4ac
Δ = -1222-4·7·(-2352)
Δ = 80740
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{80740}=\sqrt{4*20185}=\sqrt{4}*\sqrt{20185}=2\sqrt{20185}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-122)-2\sqrt{20185}}{2*7}=\frac{122-2\sqrt{20185}}{14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-122)+2\sqrt{20185}}{2*7}=\frac{122+2\sqrt{20185}}{14} $
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