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8q^2-39q-5=0
a = 8; b = -39; c = -5;
Δ = b2-4ac
Δ = -392-4·8·(-5)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{1681}=41$$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-41}{2*8}=\frac{-2}{16} =-1/8 $$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+41}{2*8}=\frac{80}{16} =5 $
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