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5000x^2+15x-16=0
a = 5000; b = 15; c = -16;
Δ = b2-4ac
Δ = 152-4·5000·(-16)
Δ = 320225
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{320225}=\sqrt{25*12809}=\sqrt{25}*\sqrt{12809}=5\sqrt{12809}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-5\sqrt{12809}}{2*5000}=\frac{-15-5\sqrt{12809}}{10000} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+5\sqrt{12809}}{2*5000}=\frac{-15+5\sqrt{12809}}{10000} $
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