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8x^2-5x-94=0
a = 8; b = -5; c = -94;
Δ = b2-4ac
Δ = -52-4·8·(-94)
Δ = 3033
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3033}=\sqrt{9*337}=\sqrt{9}*\sqrt{337}=3\sqrt{337}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3\sqrt{337}}{2*8}=\frac{5-3\sqrt{337}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3\sqrt{337}}{2*8}=\frac{5+3\sqrt{337}}{16} $
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