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4x^2+9x-47=0
a = 4; b = 9; c = -47;
Δ = b2-4ac
Δ = 92-4·4·(-47)
Δ = 833
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{833}=\sqrt{49*17}=\sqrt{49}*\sqrt{17}=7\sqrt{17}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-7\sqrt{17}}{2*4}=\frac{-9-7\sqrt{17}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+7\sqrt{17}}{2*4}=\frac{-9+7\sqrt{17}}{8} $
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