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15x^2-3x-64=0
a = 15; b = -3; c = -64;
Δ = b2-4ac
Δ = -32-4·15·(-64)
Δ = 3849
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{3849}}{2*15}=\frac{3-\sqrt{3849}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{3849}}{2*15}=\frac{3+\sqrt{3849}}{30} $
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