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7x^2-6x-976=0
a = 7; b = -6; c = -976;
Δ = b2-4ac
Δ = -62-4·7·(-976)
Δ = 27364
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{27364}=\sqrt{4*6841}=\sqrt{4}*\sqrt{6841}=2\sqrt{6841}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{6841}}{2*7}=\frac{6-2\sqrt{6841}}{14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{6841}}{2*7}=\frac{6+2\sqrt{6841}}{14} $
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