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8x^2-31x-2=0
a = 8; b = -31; c = -2;
Δ = b2-4ac
Δ = -312-4·8·(-2)
Δ = 1025
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1025}=\sqrt{25*41}=\sqrt{25}*\sqrt{41}=5\sqrt{41}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-5\sqrt{41}}{2*8}=\frac{31-5\sqrt{41}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+5\sqrt{41}}{2*8}=\frac{31+5\sqrt{41}}{16} $
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