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-16x^2+75x+6.5=0
a = -16; b = 75; c = +6.5;
Δ = b2-4ac
Δ = 752-4·(-16)·6.5
Δ = 6041
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{-(75)-\sqrt{6041}}{2*-16}=\frac{-75-\sqrt{6041}}{-32} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(75)+\sqrt{6041}}{2*-16}=\frac{-75+\sqrt{6041}}{-32} $
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