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10x^2-10x-247=0
a = 10; b = -10; c = -247;
Δ = b2-4ac
Δ = -102-4·10·(-247)
Δ = 9980
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{9980}=\sqrt{4*2495}=\sqrt{4}*\sqrt{2495}=2\sqrt{2495}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{2495}}{2*10}=\frac{10-2\sqrt{2495}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{2495}}{2*10}=\frac{10+2\sqrt{2495}}{20} $
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