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(39x^2-476x-2461)/78657=0
We multiply all the terms by the denominator
(39x^2-476x-2461)=0
We get rid of parentheses
39x^2-476x-2461=0
a = 39; b = -476; c = -2461;
Δ = b2-4ac
Δ = -4762-4·39·(-2461)
Δ = 610492
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{610492}=\sqrt{4*152623}=\sqrt{4}*\sqrt{152623}=2\sqrt{152623}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-476)-2\sqrt{152623}}{2*39}=\frac{476-2\sqrt{152623}}{78} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-476)+2\sqrt{152623}}{2*39}=\frac{476+2\sqrt{152623}}{78} $
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